Solve by Substitution 8x-3y=10 8x^2-3y^2+30y=80

$8 x - 3 y = 10$ $8 x^{2} - 3 y^{2} + 30 y = 80$

Step 1

Solve for $x$ in $8 x - 3 y = 10$ .

Add $3 y$ to both sides of the equation.

$8 x = 10 + 3 y$

$8 x^{2} - 3 y^{2} + 30 y = 80$

Divide each term in $8 x = 10 + 3 y$ by $8$ and simplify.

Divide each term in $8 x = 10 + 3 y$ by $8$ .

$\frac{8 x}{8} = \frac{10}{8} + \frac{3 y}{8}$

$8 x^{2} - 3 y^{2} + 30 y = 80$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{10}{8} + \frac{3 y}{8}$

$8 x^{2} - 3 y^{2} + 30 y = 80$

Divide $x$ by $1$ .

$x = \frac{10}{8} + \frac{3 y}{8}$

$8 x^{2} - 3 y^{2} + 30 y = 80$

$x = \frac{10}{8} + \frac{3 y}{8}$

$8 x^{2} - 3 y^{2} + 30 y = 80$

$x = \frac{10}{8} + \frac{3 y}{8}$

$8 x^{2} - 3 y^{2} + 30 y = 80$

Simplify the right side.

Cancel the common factor of $10$ and $8$ .

Factor $2$ out of $10$ .

$x = \frac{2 (5)}{8} + \frac{3 y}{8}$

$8 x^{2} - 3 y^{2} + 30 y = 80$

Cancel the common factors.

Factor $2$ out of $8$ .

$x = \frac{2 \cdot 5}{2 \cdot 4} + \frac{3 y}{8}$

$8 x^{2} - 3 y^{2} + 30 y = 80$

Cancel the common factor.

$x = \frac{2 \cdot 5}{2 \cdot 4} + \frac{3 y}{8}$

$8 x^{2} - 3 y^{2} + 30 y = 80$

Rewrite the expression.

$x = \frac{5}{4} + \frac{3 y}{8}$

$8 x^{2} - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$8 x^{2} - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$8 x^{2} - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$8 x^{2} - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$8 x^{2} - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$8 x^{2} - 3 y^{2} + 30 y = 80$

Step 2

Replace all occurrences of $x$ with $\frac{5}{4} + \frac{3 y}{8}$ in each equation.

Replace all occurrences of $x$ in $8 x^{2} - 3 y^{2} + 30 y = 80$ with $\frac{5}{4} + \frac{3 y}{8}$ .

$8 {(\frac{5}{4} + \frac{3 y}{8})}^{2} - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Simplify the left side.

Simplify $8 {(\frac{5}{4} + \frac{3 y}{8})}^{2} - 3 y^{2} + 30 y$ .

Simplify each term.

Rewrite ${(\frac{5}{4} + \frac{3 y}{8})}^{2}$ as $(\frac{5}{4} + \frac{3 y}{8}) (\frac{5}{4} + \frac{3 y}{8})$ .

$8 ((\frac{5}{4} + \frac{3 y}{8}) (\frac{5}{4} + \frac{3 y}{8})) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Expand $(\frac{5}{4} + \frac{3 y}{8}) (\frac{5}{4} + \frac{3 y}{8})$ using the FOIL Method.

Apply the distributive property.

$8 (\frac{5}{4} \cdot (\frac{5}{4} + \frac{3 y}{8}) + \frac{3 y}{8} \cdot (\frac{5}{4} + \frac{3 y}{8})) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Apply the distributive property.

$8 (\frac{5}{4} \cdot \frac{5}{4} + \frac{5}{4} \cdot \frac{3 y}{8} + \frac{3 y}{8} \cdot (\frac{5}{4} + \frac{3 y}{8})) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Apply the distributive property.

$8 (\frac{5}{4} \cdot \frac{5}{4} + \frac{5}{4} \cdot \frac{3 y}{8} + \frac{3 y}{8} \cdot \frac{5}{4} + \frac{3 y}{8} \cdot \frac{3 y}{8}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$8 (\frac{5}{4} \cdot \frac{5}{4} + \frac{5}{4} \cdot \frac{3 y}{8} + \frac{3 y}{8} \cdot \frac{5}{4} + \frac{3 y}{8} \cdot \frac{3 y}{8}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Simplify and combine like terms.

Simplify each term.

Multiply $\frac{5}{4} \cdot \frac{5}{4}$ .

Multiply $\frac{5}{4}$ by $\frac{5}{4}$ .

$8 (\frac{5 \cdot 5}{4 \cdot 4} + \frac{5}{4} \cdot \frac{3 y}{8} + \frac{3 y}{8} \cdot \frac{5}{4} + \frac{3 y}{8} \cdot \frac{3 y}{8}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Multiply $5$ by $5$ .

$8 (\frac{25}{4 \cdot 4} + \frac{5}{4} \cdot \frac{3 y}{8} + \frac{3 y}{8} \cdot \frac{5}{4} + \frac{3 y}{8} \cdot \frac{3 y}{8}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Multiply $4$ by $4$ .

$8 (\frac{25}{16} + \frac{5}{4} \cdot \frac{3 y}{8} + \frac{3 y}{8} \cdot \frac{5}{4} + \frac{3 y}{8} \cdot \frac{3 y}{8}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$8 (\frac{25}{16} + \frac{5}{4} \cdot \frac{3 y}{8} + \frac{3 y}{8} \cdot \frac{5}{4} + \frac{3 y}{8} \cdot \frac{3 y}{8}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Multiply $\frac{5}{4} \cdot \frac{3 y}{8}$ .

Multiply $\frac{5}{4}$ by $\frac{3 y}{8}$ .

$8 (\frac{25}{16} + \frac{5 (3 y)}{4 \cdot 8} + \frac{3 y}{8} \cdot \frac{5}{4} + \frac{3 y}{8} \cdot \frac{3 y}{8}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Multiply $3$ by $5$ .

$8 (\frac{25}{16} + \frac{15 y}{4 \cdot 8} + \frac{3 y}{8} \cdot \frac{5}{4} + \frac{3 y}{8} \cdot \frac{3 y}{8}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Multiply $4$ by $8$ .

$8 (\frac{25}{16} + \frac{15 y}{32} + \frac{3 y}{8} \cdot \frac{5}{4} + \frac{3 y}{8} \cdot \frac{3 y}{8}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$8 (\frac{25}{16} + \frac{15 y}{32} + \frac{3 y}{8} \cdot \frac{5}{4} + \frac{3 y}{8} \cdot \frac{3 y}{8}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Multiply $\frac{3 y}{8} \cdot \frac{5}{4}$ .

Multiply $\frac{3 y}{8}$ by $\frac{5}{4}$ .

$8 (\frac{25}{16} + \frac{15 y}{32} + \frac{3 y \cdot 5}{8 \cdot 4} + \frac{3 y}{8} \cdot \frac{3 y}{8}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Multiply $5$ by $3$ .

$8 (\frac{25}{16} + \frac{15 y}{32} + \frac{15 y}{8 \cdot 4} + \frac{3 y}{8} \cdot \frac{3 y}{8}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Multiply $8$ by $4$ .

$8 (\frac{25}{16} + \frac{15 y}{32} + \frac{15 y}{32} + \frac{3 y}{8} \cdot \frac{3 y}{8}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$8 (\frac{25}{16} + \frac{15 y}{32} + \frac{15 y}{32} + \frac{3 y}{8} \cdot \frac{3 y}{8}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Multiply $\frac{3 y}{8} \cdot \frac{3 y}{8}$ .

Multiply $\frac{3 y}{8}$ by $\frac{3 y}{8}$ .

$8 (\frac{25}{16} + \frac{15 y}{32} + \frac{15 y}{32} + \frac{3 y (3 y)}{8 \cdot 8}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Multiply $3$ by $3$ .

$8 (\frac{25}{16} + \frac{15 y}{32} + \frac{15 y}{32} + \frac{9 y \cdot y}{8 \cdot 8}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Raise $y$ to the power of $1$ .

$8 (\frac{25}{16} + \frac{15 y}{32} + \frac{15 y}{32} + \frac{9 (y \cdot y)}{8 \cdot 8}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Raise $y$ to the power of $1$ .

$8 (\frac{25}{16} + \frac{15 y}{32} + \frac{15 y}{32} + \frac{9 (y \cdot y)}{8 \cdot 8}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$8 (\frac{25}{16} + \frac{15 y}{32} + \frac{15 y}{32} + \frac{9 y^{1 + 1}}{8 \cdot 8}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Add $1$ and $1$ .

$8 (\frac{25}{16} + \frac{15 y}{32} + \frac{15 y}{32} + \frac{9 y^{2}}{8 \cdot 8}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Multiply $8$ by $8$ .

$8 (\frac{25}{16} + \frac{15 y}{32} + \frac{15 y}{32} + \frac{9 y^{2}}{64}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$8 (\frac{25}{16} + \frac{15 y}{32} + \frac{15 y}{32} + \frac{9 y^{2}}{64}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$8 (\frac{25}{16} + \frac{15 y}{32} + \frac{15 y}{32} + \frac{9 y^{2}}{64}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Add $\frac{15 y}{32}$ and $\frac{15 y}{32}$ .

$8 (\frac{25}{16} + 2 (\frac{15 y}{32}) + \frac{9 y^{2}}{64}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$8 (\frac{25}{16} + 2 (\frac{15 y}{32}) + \frac{9 y^{2}}{64}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Cancel the common factor of $2$ .

Factor $2$ out of $32$ .

$8 (\frac{25}{16} + 2 (\frac{15 y}{2 (16)}) + \frac{9 y^{2}}{64}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Cancel the common factor.

$8 (\frac{25}{16} + 2 (\frac{15 y}{2 \cdot 16}) + \frac{9 y^{2}}{64}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Rewrite the expression.

$8 (\frac{25}{16} + \frac{15 y}{16} + \frac{9 y^{2}}{64}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$8 (\frac{25}{16} + \frac{15 y}{16} + \frac{9 y^{2}}{64}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Apply the distributive property.

$8 (\frac{25}{16}) + 8 (\frac{15 y}{16}) + 8 (\frac{9 y^{2}}{64}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Simplify.

Cancel the common factor of $8$ .

Factor $8$ out of $16$ .

$8 (\frac{25}{8 (2)}) + 8 (\frac{15 y}{16}) + 8 (\frac{9 y^{2}}{64}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Cancel the common factor.

$8 (\frac{25}{8 \cdot 2}) + 8 (\frac{15 y}{16}) + 8 (\frac{9 y^{2}}{64}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Rewrite the expression.

$\frac{25}{2} + 8 (\frac{15 y}{16}) + 8 (\frac{9 y^{2}}{64}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$\frac{25}{2} + 8 (\frac{15 y}{16}) + 8 (\frac{9 y^{2}}{64}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Cancel the common factor of $8$ .

Factor $8$ out of $16$ .

$\frac{25}{2} + 8 (\frac{15 y}{8 (2)}) + 8 (\frac{9 y^{2}}{64}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Cancel the common factor.

$\frac{25}{2} + 8 (\frac{15 y}{8 \cdot 2}) + 8 (\frac{9 y^{2}}{64}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Rewrite the expression.

$\frac{25}{2} + \frac{15 y}{2} + 8 (\frac{9 y^{2}}{64}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$\frac{25}{2} + \frac{15 y}{2} + 8 (\frac{9 y^{2}}{64}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Cancel the common factor of $8$ .

Factor $8$ out of $64$ .

$\frac{25}{2} + \frac{15 y}{2} + 8 (\frac{9 y^{2}}{8 (8)}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Cancel the common factor.

$\frac{25}{2} + \frac{15 y}{2} + 8 (\frac{9 y^{2}}{8 \cdot 8}) - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Rewrite the expression.

$\frac{25}{2} + \frac{15 y}{2} + \frac{9 y^{2}}{8} - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$\frac{25}{2} + \frac{15 y}{2} + \frac{9 y^{2}}{8} - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$\frac{25}{2} + \frac{15 y}{2} + \frac{9 y^{2}}{8} - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$\frac{25}{2} + \frac{15 y}{2} + \frac{9 y^{2}}{8} - 3 y^{2} + 30 y = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

To write $30 y$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{25}{2} + \frac{9 y^{2}}{8} - 3 y^{2} + \frac{15 y}{2} + 30 y \cdot \frac{2}{2} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Combine $30 y$ and $\frac{2}{2}$ .

$\frac{25}{2} + \frac{9 y^{2}}{8} - 3 y^{2} + \frac{15 y}{2} + \frac{30 y \cdot 2}{2} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Combine the numerators over the common denominator.

$\frac{25}{2} + \frac{9 y^{2}}{8} - 3 y^{2} + \frac{15 y + 30 y \cdot 2}{2} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Combine the numerators over the common denominator.

$- 3 y^{2} + \frac{25 + 15 y + 30 y \cdot 2}{2} + \frac{9 y^{2}}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Multiply $2$ by $30$ .

$- 3 y^{2} + \frac{25 + 15 y + 60 y}{2} + \frac{9 y^{2}}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Add $15 y$ and $60 y$ .

$- 3 y^{2} + \frac{25 + 75 y}{2} + \frac{9 y^{2}}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Find the common denominator.

Write $- 3 y^{2}$ as a fraction with denominator $1$ .

$\frac{- 3 y^{2}}{1} + \frac{25 + 75 y}{2} + \frac{9 y^{2}}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Multiply $\frac{- 3 y^{2}}{1}$ by $\frac{8}{8}$ .

$\frac{- 3 y^{2}}{1} \cdot \frac{8}{8} + \frac{25 + 75 y}{2} + \frac{9 y^{2}}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Multiply $\frac{- 3 y^{2}}{1}$ by $\frac{8}{8}$ .

$\frac{- 3 y^{2} \cdot 8}{8} + \frac{25 + 75 y}{2} + \frac{9 y^{2}}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Multiply $\frac{25 + 75 y}{2}$ by $\frac{4}{4}$ .

$\frac{- 3 y^{2} \cdot 8}{8} + \frac{25 + 75 y}{2} \cdot \frac{4}{4} + \frac{9 y^{2}}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Multiply $\frac{25 + 75 y}{2}$ by $\frac{4}{4}$ .

$\frac{- 3 y^{2} \cdot 8}{8} + \frac{(25 + 75 y) \cdot 4}{2 \cdot 4} + \frac{9 y^{2}}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Multiply $2$ by $4$ .

$\frac{- 3 y^{2} \cdot 8}{8} + \frac{(25 + 75 y) \cdot 4}{8} + \frac{9 y^{2}}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$\frac{- 3 y^{2} \cdot 8}{8} + \frac{(25 + 75 y) \cdot 4}{8} + \frac{9 y^{2}}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Simplify terms.

Combine the numerators over the common denominator.

$\frac{- 3 y^{2} \cdot 8 + (25 + 75 y) \cdot 4 + 9 y^{2}}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Simplify each term.

Multiply $8$ by $- 3$ .

$\frac{- 24 y^{2} + (25 + 75 y) \cdot 4 + 9 y^{2}}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Apply the distributive property.

$\frac{- 24 y^{2} + 25 \cdot 4 + 75 y \cdot 4 + 9 y^{2}}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Multiply $25$ by $4$ .

$\frac{- 24 y^{2} + 100 + 75 y \cdot 4 + 9 y^{2}}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Multiply $4$ by $75$ .

$\frac{- 24 y^{2} + 100 + 300 y + 9 y^{2}}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$\frac{- 24 y^{2} + 100 + 300 y + 9 y^{2}}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Add $- 24 y^{2}$ and $9 y^{2}$ .

$\frac{- 15 y^{2} + 100 + 300 y}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$\frac{- 15 y^{2} + 100 + 300 y}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Simplify the numerator.

Factor $5$ out of $- 15 y^{2} + 100 + 300 y$ .

Factor $5$ out of $- 15 y^{2}$ .

$\frac{5 (- 3 y^{2}) + 100 + 300 y}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Factor $5$ out of $100$ .

$\frac{5 (- 3 y^{2}) + 5 (20) + 300 y}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Factor $5$ out of $300 y$ .

$\frac{5 (- 3 y^{2}) + 5 (20) + 5 (60 y)}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Factor $5$ out of $5 (- 3 y^{2}) + 5 (20)$ .

$\frac{5 (- 3 y^{2} + 20) + 5 (60 y)}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Factor $5$ out of $5 (- 3 y^{2} + 20) + 5 (60 y)$ .

$\frac{5 (- 3 y^{2} + 20 + 60 y)}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$\frac{5 (- 3 y^{2} + 20 + 60 y)}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Reorder terms.

$\frac{5 (- 3 y^{2} + 60 y + 20)}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$\frac{5 (- 3 y^{2} + 60 y + 20)}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Simplify with factoring out.

Factor $- 1$ out of $- 3 y^{2}$ .

$\frac{5 (- (3 y^{2}) + 60 y + 20)}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Factor $- 1$ out of $60 y$ .

$\frac{5 (- (3 y^{2}) - (- 60 y) + 20)}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Factor $- 1$ out of $- (3 y^{2}) - (- 60 y)$ .

$\frac{5 (- (3 y^{2} - 60 y) + 20)}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Rewrite $20$ as $- 1 (- 20)$ .

$\frac{5 (- (3 y^{2} - 60 y) - 1 \cdot - 20)}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Factor $- 1$ out of $- (3 y^{2} - 60 y) - 1 (- 20)$ .

$\frac{5 (- (3 y^{2} - 60 y - 20))}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Simplify the expression.

Rewrite $- (3 y^{2} - 60 y - 20)$ as $- 1 (3 y^{2} - 60 y - 20)$ .

$\frac{5 (- 1 (3 y^{2} - 60 y - 20))}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Move the negative in front of the fraction.

$- \frac{5 (3 y^{2} - 60 y - 20)}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$- \frac{5 (3 y^{2} - 60 y - 20)}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$- \frac{5 (3 y^{2} - 60 y - 20)}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$- \frac{5 (3 y^{2} - 60 y - 20)}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$- \frac{5 (3 y^{2} - 60 y - 20)}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$- \frac{5 (3 y^{2} - 60 y - 20)}{8} = 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Step 3

Solve for $y$ in $- \frac{5 (3 y^{2} - 60 y - 20)}{8} = 80$ .

Multiply both sides of the equation by $- \frac{8}{5}$ .

$- \frac{8}{5} \cdot (- \frac{5 (3 y^{2} - 60 y - 20)}{8}) = - \frac{8}{5} \cdot 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{8}{5} (- \frac{5 (3 y^{2} - 60 y - 20)}{8})$ .

Cancel the common factor of $8$ .

Move the leading negative in $- \frac{8}{5}$ into the numerator.

$\frac{- 8}{5} \cdot (- \frac{5 (3 y^{2} - 60 y - 20)}{8}) = - \frac{8}{5} \cdot 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Move the leading negative in $- \frac{5 (3 y^{2} - 60 y - 20)}{8}$ into the numerator.

$\frac{- 8}{5} \cdot \frac{- 5 (3 y^{2} - 60 y - 20)}{8} = - \frac{8}{5} \cdot 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Factor $8$ out of $- 8$ .

$\frac{8 (- 1)}{5} \cdot \frac{- 5 (3 y^{2} - 60 y - 20)}{8} = - \frac{8}{5} \cdot 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Cancel the common factor.

$\frac{8 \cdot - 1}{5} \cdot \frac{- 5 (3 y^{2} - 60 y - 20)}{8} = - \frac{8}{5} \cdot 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Rewrite the expression.

$\frac{- 1}{5} \cdot (- 5 (3 y^{2} - 60 y - 20)) = - \frac{8}{5} \cdot 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$\frac{- 1}{5} \cdot (- 5 (3 y^{2} - 60 y - 20)) = - \frac{8}{5} \cdot 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Cancel the common factor of $5$ .

Factor $5$ out of $- 5 (3 y^{2} - 60 y - 20)$ .

$\frac{- 1}{5} \cdot (5 (- (3 y^{2} - 60 y - 20))) = - \frac{8}{5} \cdot 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Cancel the common factor.

$\frac{- 1}{5} \cdot (5 (- (3 y^{2} - 60 y - 20))) = - \frac{8}{5} \cdot 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Rewrite the expression.

$3 y^{2} - 60 y - 20 = - \frac{8}{5} \cdot 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$3 y^{2} - 60 y - 20 = - \frac{8}{5} \cdot 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (3 y^{2} - 60 y - 20) = - \frac{8}{5} \cdot 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Multiply $3 y^{2} - 60 y - 20$ by $1$ .

$3 y^{2} - 60 y - 20 = - \frac{8}{5} \cdot 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$3 y^{2} - 60 y - 20 = - \frac{8}{5} \cdot 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$3 y^{2} - 60 y - 20 = - \frac{8}{5} \cdot 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

$3 y^{2} - 60 y - 20 = - \frac{8}{5} \cdot 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Simplify the right side.

Simplify $- \frac{8}{5} \cdot 80$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{8}{5}$ into the numerator.

$3 y^{2} - 60 y - 20 = \frac{- 8}{5} \cdot 80$

$x = \frac{5}{4} + \frac{3 y}{8}$

Factor $5$ out of $80$ .

$3 y^{2} - 60 y - 20 = \frac{- 8}{5} \cdot (5 (16))$

$x = \frac{5}{4} + \frac{3 y}{8}$

Cancel the common factor.

$3 y^{2} - 60 y - 20 = \frac{- 8}{5} \cdot (5 \cdot 16)$

$x = \frac{5}{4} + \frac{3 y}{8}$

Rewrite the expression.

$3 y^{2} - 60 y - 20 = - 8 \cdot 16$

$x = \frac{5}{4} + \frac{3 y}{8}$

$3 y^{2} - 60 y - 20 = - 8 \cdot 16$

$x = \frac{5}{4} + \frac{3 y}{8}$

Multiply $- 8$ by $16$ .

$3 y^{2} - 60 y - 20 = - 128$

$x = \frac{5}{4} + \frac{3 y}{8}$

$3 y^{2} - 60 y - 20 = - 128$

$x = \frac{5}{4} + \frac{3 y}{8}$

$3 y^{2} - 60 y - 20 = - 128$

$x = \frac{5}{4} + \frac{3 y}{8}$

$3 y^{2} - 60 y - 20 = - 128$

$x = \frac{5}{4} + \frac{3 y}{8}$

Add $128$ to both sides of the equation.

$3 y^{2} - 60 y - 20 + 128 = 0$

$x = \frac{5}{4} + \frac{3 y}{8}$

Add $- 20$ and $128$ .

$3 y^{2} - 60 y + 108 = 0$

$x = \frac{5}{4} + \frac{3 y}{8}$

Factor the left side of the equation.

Factor $3$ out of $3 y^{2} - 60 y + 108$ .

Factor $3$ out of $3 y^{2}$ .

$3 (y^{2}) - 60 y + 108 = 0$

$x = \frac{5}{4} + \frac{3 y}{8}$

Factor $3$ out of $- 60 y$ .

$3 (y^{2}) + 3 (- 20 y) + 108 = 0$

$x = \frac{5}{4} + \frac{3 y}{8}$

Factor $3$ out of $108$ .

$3 y^{2} + 3 (- 20 y) + 3 \cdot 36 = 0$

$x = \frac{5}{4} + \frac{3 y}{8}$

Factor $3$ out of $3 y^{2} + 3 (- 20 y)$ .

$3 (y^{2} - 20 y) + 3 \cdot 36 = 0$

$x = \frac{5}{4} + \frac{3 y}{8}$

Factor $3$ out of $3 (y^{2} - 20 y) + 3 \cdot 36$ .

$3 (y^{2} - 20 y + 36) = 0$

$x = \frac{5}{4} + \frac{3 y}{8}$

$3 (y^{2} - 20 y + 36) = 0$

$x = \frac{5}{4} + \frac{3 y}{8}$

Factor.

Factor $y^{2} - 20 y + 36$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $36$ and whose sum is $- 20$ .

$- 18, - 2$

$x = \frac{5}{4} + \frac{3 y}{8}$

Write the factored form using these integers.

$3 ((y - 18) (y - 2)) = 0$

$x = \frac{5}{4} + \frac{3 y}{8}$

$3 ((y - 18) (y - 2)) = 0$

$x = \frac{5}{4} + \frac{3 y}{8}$

Remove unnecessary parentheses.

$3 (y - 18) (y - 2) = 0$

$x = \frac{5}{4} + \frac{3 y}{8}$

$3 (y - 18) (y - 2) = 0$

$x = \frac{5}{4} + \frac{3 y}{8}$

$3 (y - 18) (y - 2) = 0$

$x = \frac{5}{4} + \frac{3 y}{8}$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$y - 18 = 0$

$y - 2 = 0$

$x = \frac{5}{4} + \frac{3 y}{8}$

Set $y - 18$ equal to $0$ and solve for $y$ .

Set $y - 18$ equal to $0$ .

$y - 18 = 0$

$x = \frac{5}{4} + \frac{3 y}{8}$

Add $18$ to both sides of the equation.

$y = 18$

$x = \frac{5}{4} + \frac{3 y}{8}$

$y = 18$

$x = \frac{5}{4} + \frac{3 y}{8}$

Set $y - 2$ equal to $0$ and solve for $y$ .

Set $y - 2$ equal to $0$ .

$y - 2 = 0$

$x = \frac{5}{4} + \frac{3 y}{8}$

Add $2$ to both sides of the equation.

$y = 2$

$x = \frac{5}{4} + \frac{3 y}{8}$

$y = 2$

$x = \frac{5}{4} + \frac{3 y}{8}$

The final solution is all the values that make $3 (y - 18) (y - 2) = 0$ true.

$y = 18, 2$

$x = \frac{5}{4} + \frac{3 y}{8}$

$y = 18, 2$

$x = \frac{5}{4} + \frac{3 y}{8}$

Step 4

Replace all occurrences of $y$ with $18$ in each equation.

Replace all occurrences of $y$ in $x = \frac{5}{4} + \frac{3 y}{8}$ with $18$ .

$x = \frac{5}{4} + \frac{3 (18)}{8}$

$y = 18$

Simplify the right side.

Simplify $\frac{5}{4} + \frac{3 (18)}{8}$ .

Multiply $3$ by $18$ .

$x = \frac{5}{4} + \frac{54}{8}$

$y = 18$

Cancel the common factor of $54$ and $8$ .

Factor $2$ out of $54$ .

$x = \frac{5}{4} + \frac{2 (27)}{8}$

$y = 18$

Cancel the common factors.

Factor $2$ out of $8$ .

$x = \frac{5}{4} + \frac{2 \cdot 27}{2 \cdot 4}$

$y = 18$

Cancel the common factor.

$x = \frac{5}{4} + \frac{2 \cdot 27}{2 \cdot 4}$

$y = 18$

Rewrite the expression.

$x = \frac{5}{4} + \frac{27}{4}$

$y = 18$

$x = \frac{5}{4} + \frac{27}{4}$

$y = 18$

$x = \frac{5}{4} + \frac{27}{4}$

$y = 18$

Combine the numerators over the common denominator.

$x = \frac{5 + 27}{4}$

$y = 18$

Simplify the expression.

Add $5$ and $27$ .

$x = \frac{32}{4}$

$y = 18$

Divide $32$ by $4$ .

$x = 8$

$y = 18$

$x = 8$

$y = 18$

$x = 8$

$y = 18$

$x = 8$

$y = 18$

$x = 8$

$y = 18$

Step 5

Replace all occurrences of $y$ with $2$ in each equation.

Replace all occurrences of $y$ in $x = \frac{5}{4} + \frac{3 y}{8}$ with $2$ .

$x = \frac{5}{4} + \frac{3 (2)}{8}$

$y = 2$

Simplify the right side.

Simplify $\frac{5}{4} + \frac{3 (2)}{8}$ .

Multiply $3$ by $2$ .

$x = \frac{5}{4} + \frac{6}{8}$

$y = 2$

Cancel the common factor of $6$ and $8$ .

Factor $2$ out of $6$ .

$x = \frac{5}{4} + \frac{2 (3)}{8}$

$y = 2$

Cancel the common factors.

Factor $2$ out of $8$ .

$x = \frac{5}{4} + \frac{2 \cdot 3}{2 \cdot 4}$

$y = 2$

Cancel the common factor.

$x = \frac{5}{4} + \frac{2 \cdot 3}{2 \cdot 4}$

$y = 2$

Rewrite the expression.

$x = \frac{5}{4} + \frac{3}{4}$

$y = 2$

$x = \frac{5}{4} + \frac{3}{4}$

$y = 2$

$x = \frac{5}{4} + \frac{3}{4}$

$y = 2$

Combine the numerators over the common denominator.

$x = \frac{5 + 3}{4}$

$y = 2$

Simplify the expression.

Add $5$ and $3$ .

$x = \frac{8}{4}$

$y = 2$

Divide $8$ by $4$ .

$x = 2$

$y = 2$

$x = 2$

$y = 2$

$x = 2$

$y = 2$

$x = 2$

$y = 2$

$x = 2$

$y = 2$

Step 6

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(8, 18)$

$(2, 2)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(8, 18), (2, 2)$

Equation Form:

$x = 8, y = 18$

$x = 2, y = 2$

Step 8

Solve by Substitution 8x-3y=10 8x^2-3y^2+30y=80

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