Solve the System of Equations x^2+y^2=68 5y=-3x+34

$x^{2} + y^{2} = 68$ $5 y = - 3 x + 34$

Divide each term in $5 y = - 3 x + 34$ by $5$ and simplify.

Divide each term in $5 y = - 3 x + 34$ by $5$ .

$\frac{5 y}{5} = \frac{- 3 x}{5} + \frac{34}{5}$

$x^{2} + y^{2} = 68$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{- 3 x}{5} + \frac{34}{5}$

$x^{2} + y^{2} = 68$

Divide $y$ by $1$ .

$y = \frac{- 3 x}{5} + \frac{34}{5}$

$x^{2} + y^{2} = 68$

$y = \frac{- 3 x}{5} + \frac{34}{5}$

$x^{2} + y^{2} = 68$

$y = \frac{- 3 x}{5} + \frac{34}{5}$

$x^{2} + y^{2} = 68$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{3 x}{5} + \frac{34}{5}$

$x^{2} + y^{2} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$x^{2} + y^{2} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$x^{2} + y^{2} = 68$

Replace all occurrences of $y$ with $- \frac{3 x}{5} + \frac{34}{5}$ in each equation.

Replace all occurrences of $y$ in $x^{2} + y^{2} = 68$ with $- \frac{3 x}{5} + \frac{34}{5}$ .

$x^{2} + {(- \frac{3 x}{5} + \frac{34}{5})}^{2} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Simplify the left side.

Simplify $x^{2} + {(- \frac{3 x}{5} + \frac{34}{5})}^{2}$ .

Simplify each term.

Rewrite ${(- \frac{3 x}{5} + \frac{34}{5})}^{2}$ as $(- \frac{3 x}{5} + \frac{34}{5}) (- \frac{3 x}{5} + \frac{34}{5})$ .

$x^{2} + (- \frac{3 x}{5} + \frac{34}{5}) (- \frac{3 x}{5} + \frac{34}{5}) = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Expand $(- \frac{3 x}{5} + \frac{34}{5}) (- \frac{3 x}{5} + \frac{34}{5})$ using the FOIL Method.

Apply the distributive property.

$x^{2} - \frac{3 x}{5} \cdot (- \frac{3 x}{5} + \frac{34}{5}) + \frac{34}{5} \cdot (- \frac{3 x}{5} + \frac{34}{5}) = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Apply the distributive property.

$x^{2} - \frac{3 x}{5} \cdot (- \frac{3 x}{5}) - \frac{3 x}{5} \cdot \frac{34}{5} + \frac{34}{5} \cdot (- \frac{3 x}{5} + \frac{34}{5}) = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Apply the distributive property.

$x^{2} - \frac{3 x}{5} \cdot (- \frac{3 x}{5}) - \frac{3 x}{5} \cdot \frac{34}{5} + \frac{34}{5} \cdot (- \frac{3 x}{5}) + \frac{34}{5} \cdot \frac{34}{5} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$x^{2} - \frac{3 x}{5} \cdot (- \frac{3 x}{5}) - \frac{3 x}{5} \cdot \frac{34}{5} + \frac{34}{5} \cdot (- \frac{3 x}{5}) + \frac{34}{5} \cdot \frac{34}{5} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Simplify and combine like terms.

Simplify each term.

Multiply $- \frac{3 x}{5} (- \frac{3 x}{5})$ .

Multiply $- 1$ by $- 1$ .

$x^{2} + 1 (\frac{3 x}{5}) \cdot \frac{3 x}{5} - \frac{3 x}{5} \cdot \frac{34}{5} + \frac{34}{5} \cdot (- \frac{3 x}{5}) + \frac{34}{5} \cdot \frac{34}{5} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Multiply $\frac{3 x}{5}$ by $1$ .

$x^{2} + \frac{3 x}{5} \cdot \frac{3 x}{5} - \frac{3 x}{5} \cdot \frac{34}{5} + \frac{34}{5} \cdot (- \frac{3 x}{5}) + \frac{34}{5} \cdot \frac{34}{5} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Multiply $\frac{3 x}{5}$ by $\frac{3 x}{5}$ .

$x^{2} + \frac{3 x (3 x)}{5 \cdot 5} - \frac{3 x}{5} \cdot \frac{34}{5} + \frac{34}{5} \cdot (- \frac{3 x}{5}) + \frac{34}{5} \cdot \frac{34}{5} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Multiply $3$ by $3$ .

$x^{2} + \frac{9 x \cdot x}{5 \cdot 5} - \frac{3 x}{5} \cdot \frac{34}{5} + \frac{34}{5} \cdot (- \frac{3 x}{5}) + \frac{34}{5} \cdot \frac{34}{5} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

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

$x^{2} + \frac{9 (x \cdot x)}{5 \cdot 5} - \frac{3 x}{5} \cdot \frac{34}{5} + \frac{34}{5} \cdot (- \frac{3 x}{5}) + \frac{34}{5} \cdot \frac{34}{5} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

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

$x^{2} + \frac{9 (x \cdot x)}{5 \cdot 5} - \frac{3 x}{5} \cdot \frac{34}{5} + \frac{34}{5} \cdot (- \frac{3 x}{5}) + \frac{34}{5} \cdot \frac{34}{5} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

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

$x^{2} + \frac{9 x^{1 + 1}}{5 \cdot 5} - \frac{3 x}{5} \cdot \frac{34}{5} + \frac{34}{5} \cdot (- \frac{3 x}{5}) + \frac{34}{5} \cdot \frac{34}{5} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Add $1$ and $1$ .

$x^{2} + \frac{9 x^{2}}{5 \cdot 5} - \frac{3 x}{5} \cdot \frac{34}{5} + \frac{34}{5} \cdot (- \frac{3 x}{5}) + \frac{34}{5} \cdot \frac{34}{5} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Multiply $5$ by $5$ .

$x^{2} + \frac{9 x^{2}}{25} - \frac{3 x}{5} \cdot \frac{34}{5} + \frac{34}{5} \cdot (- \frac{3 x}{5}) + \frac{34}{5} \cdot \frac{34}{5} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$x^{2} + \frac{9 x^{2}}{25} - \frac{3 x}{5} \cdot \frac{34}{5} + \frac{34}{5} \cdot (- \frac{3 x}{5}) + \frac{34}{5} \cdot \frac{34}{5} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Multiply $- \frac{3 x}{5} \cdot \frac{34}{5}$ .

Multiply $\frac{34}{5}$ by $\frac{3 x}{5}$ .

$x^{2} + \frac{9 x^{2}}{25} - \frac{34 (3 x)}{5 \cdot 5} + \frac{34}{5} \cdot (- \frac{3 x}{5}) + \frac{34}{5} \cdot \frac{34}{5} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Multiply $3$ by $34$ .

$x^{2} + \frac{9 x^{2}}{25} - \frac{102 x}{5 \cdot 5} + \frac{34}{5} \cdot (- \frac{3 x}{5}) + \frac{34}{5} \cdot \frac{34}{5} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Multiply $5$ by $5$ .

$x^{2} + \frac{9 x^{2}}{25} - \frac{102 x}{25} + \frac{34}{5} \cdot (- \frac{3 x}{5}) + \frac{34}{5} \cdot \frac{34}{5} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$x^{2} + \frac{9 x^{2}}{25} - \frac{102 x}{25} + \frac{34}{5} \cdot (- \frac{3 x}{5}) + \frac{34}{5} \cdot \frac{34}{5} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Multiply $\frac{34}{5} (- \frac{3 x}{5})$ .

Multiply $\frac{34}{5}$ by $\frac{3 x}{5}$ .

$x^{2} + \frac{9 x^{2}}{25} - \frac{102 x}{25} - \frac{34 (3 x)}{5 \cdot 5} + \frac{34}{5} \cdot \frac{34}{5} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Multiply $3$ by $34$ .

$x^{2} + \frac{9 x^{2}}{25} - \frac{102 x}{25} - \frac{102 x}{5 \cdot 5} + \frac{34}{5} \cdot \frac{34}{5} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Multiply $5$ by $5$ .

$x^{2} + \frac{9 x^{2}}{25} - \frac{102 x}{25} - \frac{102 x}{25} + \frac{34}{5} \cdot \frac{34}{5} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$x^{2} + \frac{9 x^{2}}{25} - \frac{102 x}{25} - \frac{102 x}{25} + \frac{34}{5} \cdot \frac{34}{5} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Multiply $\frac{34}{5} \cdot \frac{34}{5}$ .

Multiply $\frac{34}{5}$ by $\frac{34}{5}$ .

$x^{2} + \frac{9 x^{2}}{25} - \frac{102 x}{25} - \frac{102 x}{25} + \frac{34 \cdot 34}{5 \cdot 5} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Multiply $34$ by $34$ .

$x^{2} + \frac{9 x^{2}}{25} - \frac{102 x}{25} - \frac{102 x}{25} + \frac{1156}{5 \cdot 5} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Multiply $5$ by $5$ .

$x^{2} + \frac{9 x^{2}}{25} - \frac{102 x}{25} - \frac{102 x}{25} + \frac{1156}{25} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$x^{2} + \frac{9 x^{2}}{25} - \frac{102 x}{25} - \frac{102 x}{25} + \frac{1156}{25} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$x^{2} + \frac{9 x^{2}}{25} - \frac{102 x}{25} - \frac{102 x}{25} + \frac{1156}{25} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Subtract $\frac{102 x}{25}$ from $- \frac{102 x}{25}$ .

$x^{2} + \frac{9 x^{2}}{25} - 2 \frac{102 x}{25} + \frac{1156}{25} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$x^{2} + \frac{9 x^{2}}{25} - 2 \frac{102 x}{25} + \frac{1156}{25} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Simplify each term.

Multiply $- 2 \frac{102 x}{25}$ .

Combine $- 2$ and $\frac{102 x}{25}$ .

$x^{2} + \frac{9 x^{2}}{25} + \frac{- 2 (102 x)}{25} + \frac{1156}{25} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Multiply $102$ by $- 2$ .

$x^{2} + \frac{9 x^{2}}{25} + \frac{- 204 x}{25} + \frac{1156}{25} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$x^{2} + \frac{9 x^{2}}{25} + \frac{- 204 x}{25} + \frac{1156}{25} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Move the negative in front of the fraction.

$x^{2} + \frac{9 x^{2}}{25} - \frac{204 x}{25} + \frac{1156}{25} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$x^{2} + \frac{9 x^{2}}{25} - \frac{204 x}{25} + \frac{1156}{25} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$x^{2} + \frac{9 x^{2}}{25} - \frac{204 x}{25} + \frac{1156}{25} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

To write $x^{2}$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

$x^{2} \cdot \frac{25}{25} + \frac{9 x^{2}}{25} - \frac{204 x}{25} + \frac{1156}{25} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Simplify terms.

Combine $x^{2}$ and $\frac{25}{25}$ .

$\frac{x^{2} \cdot 25}{25} + \frac{9 x^{2}}{25} - \frac{204 x}{25} + \frac{1156}{25} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Combine the numerators over the common denominator.

$\frac{x^{2} \cdot 25 + 9 x^{2}}{25} - \frac{204 x}{25} + \frac{1156}{25} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Combine the numerators over the common denominator.

$\frac{x^{2} \cdot 25 + 9 x^{2} - 204 x + 1156}{25} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$\frac{x^{2} \cdot 25 + 9 x^{2} - 204 x + 1156}{25} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Move $25$ to the left of $x^{2}$ .

$\frac{25 x^{2} + 9 x^{2} - 204 x + 1156}{25} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Simplify terms.

Add $25 x^{2}$ and $9 x^{2}$ .

$\frac{34 x^{2} - 204 x + 1156}{25} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Factor $34$ out of $34 x^{2} - 204 x + 1156$ .

Factor $34$ out of $34 x^{2}$ .

$\frac{34 (x^{2}) - 204 x + 1156}{25} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Factor $34$ out of $- 204 x$ .

$\frac{34 (x^{2}) + 34 (- 6 x) + 1156}{25} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Factor $34$ out of $1156$ .

$\frac{34 x^{2} + 34 (- 6 x) + 34 \cdot 34}{25} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Factor $34$ out of $34 x^{2} + 34 (- 6 x)$ .

$\frac{34 (x^{2} - 6 x) + 34 \cdot 34}{25} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Factor $34$ out of $34 (x^{2} - 6 x) + 34 \cdot 34$ .

$\frac{34 (x^{2} - 6 x + 34)}{25} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$\frac{34 (x^{2} - 6 x + 34)}{25} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$\frac{34 (x^{2} - 6 x + 34)}{25} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$\frac{34 (x^{2} - 6 x + 34)}{25} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$\frac{34 (x^{2} - 6 x + 34)}{25} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$\frac{34 (x^{2} - 6 x + 34)}{25} = 68$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Solve for $x$ in $\frac{34 (x^{2} - 6 x + 34)}{25} = 68$ .

Multiply both sides by $25$ .

$\frac{34 (x^{2} - 6 x + 34)}{25} \cdot 25 = 68 \cdot 25$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Simplify.

Simplify the left side.

Simplify $\frac{34 (x^{2} - 6 x + 34)}{25} \cdot 25$ .

Cancel the common factor of $25$ .

Cancel the common factor.

$\frac{34 (x^{2} - 6 x + 34)}{25} \cdot 25 = 68 \cdot 25$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Rewrite the expression.

$34 (x^{2} - 6 x + 34) = 68 \cdot 25$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$34 (x^{2} - 6 x + 34) = 68 \cdot 25$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Apply the distributive property.

$34 x^{2} + 34 (- 6 x) + 34 \cdot 34 = 68 \cdot 25$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Simplify.

Multiply $- 6$ by $34$ .

$34 x^{2} - 204 x + 34 \cdot 34 = 68 \cdot 25$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Multiply $34$ by $34$ .

$34 x^{2} - 204 x + 1156 = 68 \cdot 25$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$34 x^{2} - 204 x + 1156 = 68 \cdot 25$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$34 x^{2} - 204 x + 1156 = 68 \cdot 25$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$34 x^{2} - 204 x + 1156 = 68 \cdot 25$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Simplify the right side.

Multiply $68$ by $25$ .

$34 x^{2} - 204 x + 1156 = 1700$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$34 x^{2} - 204 x + 1156 = 1700$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$34 x^{2} - 204 x + 1156 = 1700$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Solve for $x$ .

Subtract $1700$ from both sides of the equation.

$34 x^{2} - 204 x + 1156 - 1700 = 0$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Subtract $1700$ from $1156$ .

$34 x^{2} - 204 x - 544 = 0$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Factor the left side of the equation.

Factor $34$ out of $34 x^{2} - 204 x - 544$ .

Factor $34$ out of $34 x^{2}$ .

$34 (x^{2}) - 204 x - 544 = 0$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Factor $34$ out of $- 204 x$ .

$34 (x^{2}) + 34 (- 6 x) - 544 = 0$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Factor $34$ out of $- 544$ .

$34 x^{2} + 34 (- 6 x) + 34 \cdot - 16 = 0$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Factor $34$ out of $34 x^{2} + 34 (- 6 x)$ .

$34 (x^{2} - 6 x) + 34 \cdot - 16 = 0$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Factor $34$ out of $34 (x^{2} - 6 x) + 34 \cdot - 16$ .

$34 (x^{2} - 6 x - 16) = 0$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$34 (x^{2} - 6 x - 16) = 0$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Factor.

Factor $x^{2} - 6 x - 16$ 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 $- 16$ and whose sum is $- 6$ .

$- 8, 2$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Write the factored form using these integers.

$34 ((x - 8) (x + 2)) = 0$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$34 ((x - 8) (x + 2)) = 0$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Remove unnecessary parentheses.

$34 (x - 8) (x + 2) = 0$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$34 (x - 8) (x + 2) = 0$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$34 (x - 8) (x + 2) = 0$

$y = - \frac{3 x}{5} + \frac{34}{5}$

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

$x - 8 = 0$

$x + 2 = 0$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Set $x - 8$ equal to $0$ and solve for $x$ .

Set $x - 8$ equal to $0$ .

$x - 8 = 0$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Add $8$ to both sides of the equation.

$x = 8$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$x = 8$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Set $x + 2$ equal to $0$ and solve for $x$ .

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Subtract $2$ from both sides of the equation.

$x = - 2$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$x = - 2$

$y = - \frac{3 x}{5} + \frac{34}{5}$

The final solution is all the values that make $34 (x - 8) (x + 2) = 0$ true.

$x = 8, - 2$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$x = 8, - 2$

$y = - \frac{3 x}{5} + \frac{34}{5}$

$x = 8, - 2$

$y = - \frac{3 x}{5} + \frac{34}{5}$

Replace all occurrences of $x$ with $8$ in each equation.

Replace all occurrences of $x$ in $y = - \frac{3 x}{5} + \frac{34}{5}$ with $8$ .

$y = - \frac{3 (8)}{5} + \frac{34}{5}$

$x = 8$

Simplify the right side.

Simplify $- \frac{3 (8)}{5} + \frac{34}{5}$ .

Combine the numerators over the common denominator.

$y = \frac{- 3 \cdot 8 + 34}{5}$

$x = 8$

Simplify the expression.

Multiply $- 3$ by $8$ .

$y = \frac{- 24 + 34}{5}$

$x = 8$

Add $- 24$ and $34$ .

$y = \frac{10}{5}$

$x = 8$

Divide $10$ by $5$ .

$y = 2$

$x = 8$

$y = 2$

$x = 8$

$y = 2$

$x = 8$

$y = 2$

$x = 8$

$y = 2$

$x = 8$

Replace all occurrences of $x$ with $- 2$ in each equation.

Replace all occurrences of $x$ in $y = - \frac{3 x}{5} + \frac{34}{5}$ with $- 2$ .

$y = - \frac{3 (- 2)}{5} + \frac{34}{5}$

$x = - 2$

Simplify the right side.

Simplify $- \frac{3 (- 2)}{5} + \frac{34}{5}$ .

Combine the numerators over the common denominator.

$y = \frac{- 3 \cdot - 2 + 34}{5}$

$x = - 2$

Simplify the expression.

Multiply $- 3$ by $- 2$ .

$y = \frac{6 + 34}{5}$

$x = - 2$

Add $6$ and $34$ .

$y = \frac{40}{5}$

$x = - 2$

Divide $40$ by $5$ .

$y = 8$

$x = - 2$

$y = 8$

$x = - 2$

$y = 8$

$x = - 2$

$y = 8$

$x = - 2$

$y = 8$

$x = - 2$

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

$(8, 2)$

$(- 2, 8)$

The result can be shown in multiple forms.

Point Form:

$(8, 2), (- 2, 8)$

Equation Form:

$x = 8, y = 2$

$x = - 2, y = 8$

Solve the System of Equations x^2+y^2=68 5y=-3x+34

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