Solve the System of Equations -10/3x+1/8y=-87/8 7/10x-4y=301/10

$- \frac{10}{3} x + \frac{1}{8} y = - \frac{87}{8}$ $\frac{7}{10} x - 4 y = \frac{301}{10}$

Step 1

Solve for $y$ in $\frac{7}{10} x - 4 y = \frac{301}{10}$ .

Combine $\frac{7}{10}$ and $x$ .

$\frac{7 x}{10} - 4 y = \frac{301}{10}$

$- \frac{10}{3} x + \frac{1}{8} y = - \frac{87}{8}$

Subtract $\frac{7 x}{10}$ from both sides of the equation.

$- 4 y = \frac{301}{10} - \frac{7 x}{10}$

$- \frac{10}{3} x + \frac{1}{8} y = - \frac{87}{8}$

Divide each term in $- 4 y = \frac{301}{10} - \frac{7 x}{10}$ by $- 4$ and simplify.

Divide each term in $- 4 y = \frac{301}{10} - \frac{7 x}{10}$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{\frac{301}{10}}{- 4} + \frac{- \frac{7 x}{10}}{- 4}$

$- \frac{10}{3} x + \frac{1}{8} y = - \frac{87}{8}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{\frac{301}{10}}{- 4} + \frac{- \frac{7 x}{10}}{- 4}$

$- \frac{10}{3} x + \frac{1}{8} y = - \frac{87}{8}$

Divide $y$ by $1$ .

$y = \frac{\frac{301}{10}}{- 4} + \frac{- \frac{7 x}{10}}{- 4}$

$- \frac{10}{3} x + \frac{1}{8} y = - \frac{87}{8}$

$y = \frac{\frac{301}{10}}{- 4} + \frac{- \frac{7 x}{10}}{- 4}$

$- \frac{10}{3} x + \frac{1}{8} y = - \frac{87}{8}$

$y = \frac{\frac{301}{10}}{- 4} + \frac{- \frac{7 x}{10}}{- 4}$

$- \frac{10}{3} x + \frac{1}{8} y = - \frac{87}{8}$

Simplify the right side.

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{301}{10} \cdot \frac{1}{- 4} + \frac{- \frac{7 x}{10}}{- 4}$

$- \frac{10}{3} x + \frac{1}{8} y = - \frac{87}{8}$

Move the negative in front of the fraction.

$y = \frac{301}{10} \cdot (- \frac{1}{4}) + \frac{- \frac{7 x}{10}}{- 4}$

$- \frac{10}{3} x + \frac{1}{8} y = - \frac{87}{8}$

Multiply $\frac{301}{10} (- \frac{1}{4})$ .

Multiply $\frac{301}{10}$ by $\frac{1}{4}$ .

$y = - \frac{301}{10 \cdot 4} + \frac{- \frac{7 x}{10}}{- 4}$

$- \frac{10}{3} x + \frac{1}{8} y = - \frac{87}{8}$

Multiply $10$ by $4$ .

$y = - \frac{301}{40} + \frac{- \frac{7 x}{10}}{- 4}$

$- \frac{10}{3} x + \frac{1}{8} y = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{- \frac{7 x}{10}}{- 4}$

$- \frac{10}{3} x + \frac{1}{8} y = - \frac{87}{8}$

Multiply the numerator by the reciprocal of the denominator.

$y = - \frac{301}{40} - \frac{7 x}{10} \cdot \frac{1}{- 4}$

$- \frac{10}{3} x + \frac{1}{8} y = - \frac{87}{8}$

Move the negative in front of the fraction.

$y = - \frac{301}{40} - \frac{7 x}{10} \cdot (- \frac{1}{4})$

$- \frac{10}{3} x + \frac{1}{8} y = - \frac{87}{8}$

Multiply $- \frac{7 x}{10} (- \frac{1}{4})$ .

Multiply $- 1$ by $- 1$ .

$y = - \frac{301}{40} + 1 (\frac{7 x}{10}) \cdot \frac{1}{4}$

$- \frac{10}{3} x + \frac{1}{8} y = - \frac{87}{8}$

Multiply $\frac{7 x}{10}$ by $1$ .

$y = - \frac{301}{40} + \frac{7 x}{10} \cdot \frac{1}{4}$

$- \frac{10}{3} x + \frac{1}{8} y = - \frac{87}{8}$

Multiply $\frac{7 x}{10}$ by $\frac{1}{4}$ .

$y = - \frac{301}{40} + \frac{7 x}{10 \cdot 4}$

$- \frac{10}{3} x + \frac{1}{8} y = - \frac{87}{8}$

Multiply $10$ by $4$ .

$y = - \frac{301}{40} + \frac{7 x}{40}$

$- \frac{10}{3} x + \frac{1}{8} y = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

$- \frac{10}{3} x + \frac{1}{8} y = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

$- \frac{10}{3} x + \frac{1}{8} y = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

$- \frac{10}{3} x + \frac{1}{8} y = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

$- \frac{10}{3} x + \frac{1}{8} y = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

$- \frac{10}{3} x + \frac{1}{8} y = - \frac{87}{8}$

Step 2

Replace all occurrences of $y$ with $- \frac{301}{40} + \frac{7 x}{40}$ in each equation.

Replace all occurrences of $y$ in $- \frac{10}{3} x + \frac{1}{8} y = - \frac{87}{8}$ with $- \frac{301}{40} + \frac{7 x}{40}$ .

$- \frac{10}{3} x + \frac{1}{8} \cdot (- \frac{301}{40} + \frac{7 x}{40}) = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Simplify the left side.

Simplify $- \frac{10}{3} x + \frac{1}{8} \cdot (- \frac{301}{40} + \frac{7 x}{40})$ .

Simplify each term.

Combine $x$ and $\frac{10}{3}$ .

$- \frac{x \cdot 10}{3} + \frac{1}{8} \cdot (- \frac{301}{40} + \frac{7 x}{40}) = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Move $10$ to the left of $x$ .

$- \frac{10 \cdot x}{3} + \frac{1}{8} \cdot (- \frac{301}{40} + \frac{7 x}{40}) = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Apply the distributive property.

$- \frac{10 x}{3} + \frac{1}{8} \cdot (- \frac{301}{40}) + \frac{1}{8} \cdot \frac{7 x}{40} = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Multiply $\frac{1}{8} (- \frac{301}{40})$ .

Multiply $\frac{1}{8}$ by $\frac{301}{40}$ .

$- \frac{10 x}{3} - \frac{301}{8 \cdot 40} + \frac{1}{8} \cdot \frac{7 x}{40} = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Multiply $8$ by $40$ .

$- \frac{10 x}{3} - \frac{301}{320} + \frac{1}{8} \cdot \frac{7 x}{40} = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

$- \frac{10 x}{3} - \frac{301}{320} + \frac{1}{8} \cdot \frac{7 x}{40} = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Multiply $\frac{1}{8} \cdot \frac{7 x}{40}$ .

Multiply $\frac{1}{8}$ by $\frac{7 x}{40}$ .

$- \frac{10 x}{3} - \frac{301}{320} + \frac{7 x}{8 \cdot 40} = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Multiply $8$ by $40$ .

$- \frac{10 x}{3} - \frac{301}{320} + \frac{7 x}{320} = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

$- \frac{10 x}{3} - \frac{301}{320} + \frac{7 x}{320} = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

$- \frac{10 x}{3} - \frac{301}{320} + \frac{7 x}{320} = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

To write $- \frac{10 x}{3}$ as a fraction with a common denominator, multiply by $\frac{320}{320}$ .

$- \frac{10 x}{3} \cdot \frac{320}{320} + \frac{7 x}{320} - \frac{301}{320} = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

To write $\frac{7 x}{320}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{10 x}{3} \cdot \frac{320}{320} + \frac{7 x}{320} \cdot \frac{3}{3} - \frac{301}{320} = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Write each expression with a common denominator of $960$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{10 x}{3}$ by $\frac{320}{320}$ .

$- \frac{10 x \cdot 320}{3 \cdot 320} + \frac{7 x}{320} \cdot \frac{3}{3} - \frac{301}{320} = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Multiply $3$ by $320$ .

$- \frac{10 x \cdot 320}{960} + \frac{7 x}{320} \cdot \frac{3}{3} - \frac{301}{320} = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Multiply $\frac{7 x}{320}$ by $\frac{3}{3}$ .

$- \frac{10 x \cdot 320}{960} + \frac{7 x \cdot 3}{320 \cdot 3} - \frac{301}{320} = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Multiply $320$ by $3$ .

$- \frac{10 x \cdot 320}{960} + \frac{7 x \cdot 3}{960} - \frac{301}{320} = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

$- \frac{10 x \cdot 320}{960} + \frac{7 x \cdot 3}{960} - \frac{301}{320} = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Combine the numerators over the common denominator.

$\frac{- 10 x \cdot 320 + 7 x \cdot 3}{960} - \frac{301}{320} = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $- 10 x \cdot 320 + 7 x \cdot 3$ .

Factor $x$ out of $- 10 x \cdot 320$ .

$\frac{x (- 10 \cdot 320) + 7 x \cdot 3}{960} - \frac{301}{320} = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Factor $x$ out of $7 x \cdot 3$ .

$\frac{x (- 10 \cdot 320) + x (7 \cdot 3)}{960} - \frac{301}{320} = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Factor $x$ out of $x (- 10 \cdot 320) + x (7 \cdot 3)$ .

$\frac{x (- 10 \cdot 320 + 7 \cdot 3)}{960} - \frac{301}{320} = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

$\frac{x (- 10 \cdot 320 + 7 \cdot 3)}{960} - \frac{301}{320} = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Multiply $- 10$ by $320$ .

$\frac{x (- 3200 + 7 \cdot 3)}{960} - \frac{301}{320} = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Multiply $7$ by $3$ .

$\frac{x (- 3200 + 21)}{960} - \frac{301}{320} = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Add $- 3200$ and $21$ .

$\frac{x \cdot - 3179}{960} - \frac{301}{320} = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

$\frac{x \cdot - 3179}{960} - \frac{301}{320} = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Move $- 3179$ to the left of $x$ .

$\frac{- 3179 \cdot x}{960} - \frac{301}{320} = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Move the negative in front of the fraction.

$- \frac{3179 x}{960} - \frac{301}{320} = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

$- \frac{3179 x}{960} - \frac{301}{320} = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

$- \frac{3179 x}{960} - \frac{301}{320} = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

$- \frac{3179 x}{960} - \frac{301}{320} = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

$- \frac{3179 x}{960} - \frac{301}{320} = - \frac{87}{8}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Step 3

Solve for $x$ in $- \frac{3179 x}{960} - \frac{301}{320} = - \frac{87}{8}$ .

Move all terms not containing $x$ to the right side of the equation.

Add $\frac{301}{320}$ to both sides of the equation.

$- \frac{3179 x}{960} = - \frac{87}{8} + \frac{301}{320}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

To write $- \frac{87}{8}$ as a fraction with a common denominator, multiply by $\frac{40}{40}$ .

$- \frac{3179 x}{960} = - \frac{87}{8} \cdot \frac{40}{40} + \frac{301}{320}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Write each expression with a common denominator of $320$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{87}{8}$ by $\frac{40}{40}$ .

$- \frac{3179 x}{960} = - \frac{87 \cdot 40}{8 \cdot 40} + \frac{301}{320}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Multiply $8$ by $40$ .

$- \frac{3179 x}{960} = - \frac{87 \cdot 40}{320} + \frac{301}{320}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

$- \frac{3179 x}{960} = - \frac{87 \cdot 40}{320} + \frac{301}{320}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Combine the numerators over the common denominator.

$- \frac{3179 x}{960} = \frac{- 87 \cdot 40 + 301}{320}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Simplify the numerator.

Multiply $- 87$ by $40$ .

$- \frac{3179 x}{960} = \frac{- 3480 + 301}{320}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Add $- 3480$ and $301$ .

$- \frac{3179 x}{960} = \frac{- 3179}{320}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

$- \frac{3179 x}{960} = \frac{- 3179}{320}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Move the negative in front of the fraction.

$- \frac{3179 x}{960} = - \frac{3179}{320}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

$- \frac{3179 x}{960} = - \frac{3179}{320}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Multiply both sides of the equation by $- \frac{960}{3179}$ .

$- \frac{960}{3179} \cdot (- \frac{3179 x}{960}) = - \frac{960}{3179} \cdot (- \frac{3179}{320})$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{960}{3179} (- \frac{3179 x}{960})$ .

Cancel the common factor of $960$ .

Move the leading negative in $- \frac{960}{3179}$ into the numerator.

$\frac{- 960}{3179} \cdot (- \frac{3179 x}{960}) = - \frac{960}{3179} \cdot (- \frac{3179}{320})$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Move the leading negative in $- \frac{3179 x}{960}$ into the numerator.

$\frac{- 960}{3179} \cdot \frac{- 3179 x}{960} = - \frac{960}{3179} \cdot (- \frac{3179}{320})$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Factor $960$ out of $- 960$ .

$\frac{960 (- 1)}{3179} \cdot \frac{- 3179 x}{960} = - \frac{960}{3179} \cdot (- \frac{3179}{320})$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Cancel the common factor.

$\frac{960 \cdot - 1}{3179} \cdot \frac{- 3179 x}{960} = - \frac{960}{3179} \cdot (- \frac{3179}{320})$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Rewrite the expression.

$\frac{- 1}{3179} \cdot (- 3179 x) = - \frac{960}{3179} \cdot (- \frac{3179}{320})$

$y = - \frac{301}{40} + \frac{7 x}{40}$

$\frac{- 1}{3179} \cdot (- 3179 x) = - \frac{960}{3179} \cdot (- \frac{3179}{320})$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Cancel the common factor of $3179$ .

Factor $3179$ out of $- 3179 x$ .

$\frac{- 1}{3179} \cdot (3179 (- x)) = - \frac{960}{3179} \cdot (- \frac{3179}{320})$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Cancel the common factor.

$\frac{- 1}{3179} \cdot (3179 (- x)) = - \frac{960}{3179} \cdot (- \frac{3179}{320})$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Rewrite the expression.

$x = - \frac{960}{3179} \cdot (- \frac{3179}{320})$

$y = - \frac{301}{40} + \frac{7 x}{40}$

$x = - \frac{960}{3179} \cdot (- \frac{3179}{320})$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{960}{3179} \cdot (- \frac{3179}{320})$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Multiply $x$ by $1$ .

$x = - \frac{960}{3179} \cdot (- \frac{3179}{320})$

$y = - \frac{301}{40} + \frac{7 x}{40}$

$x = - \frac{960}{3179} \cdot (- \frac{3179}{320})$

$y = - \frac{301}{40} + \frac{7 x}{40}$

$x = - \frac{960}{3179} \cdot (- \frac{3179}{320})$

$y = - \frac{301}{40} + \frac{7 x}{40}$

$x = - \frac{960}{3179} \cdot (- \frac{3179}{320})$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Simplify the right side.

Simplify $- \frac{960}{3179} (- \frac{3179}{320})$ .

Cancel the common factor of $320$ .

Move the leading negative in $- \frac{960}{3179}$ into the numerator.

$x = \frac{- 960}{3179} \cdot (- \frac{3179}{320})$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Move the leading negative in $- \frac{3179}{320}$ into the numerator.

$x = \frac{- 960}{3179} \cdot \frac{- 3179}{320}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Factor $320$ out of $- 960$ .

$x = \frac{320 (- 3)}{3179} \cdot \frac{- 3179}{320}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Cancel the common factor.

$x = \frac{320 \cdot - 3}{3179} \cdot \frac{- 3179}{320}$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Rewrite the expression.

$x = \frac{- 3}{3179} \cdot - 3179$

$y = - \frac{301}{40} + \frac{7 x}{40}$

$x = \frac{- 3}{3179} \cdot - 3179$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Cancel the common factor of $3179$ .

Factor $3179$ out of $- 3179$ .

$x = \frac{- 3}{3179} \cdot (3179 (- 1))$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Cancel the common factor.

$x = \frac{- 3}{3179} \cdot (3179 \cdot - 1)$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Rewrite the expression.

$x = - 3 \cdot - 1$

$y = - \frac{301}{40} + \frac{7 x}{40}$

$x = - 3 \cdot - 1$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Multiply $- 3$ by $- 1$ .

$x = 3$

$y = - \frac{301}{40} + \frac{7 x}{40}$

$x = 3$

$y = - \frac{301}{40} + \frac{7 x}{40}$

$x = 3$

$y = - \frac{301}{40} + \frac{7 x}{40}$

$x = 3$

$y = - \frac{301}{40} + \frac{7 x}{40}$

$x = 3$

$y = - \frac{301}{40} + \frac{7 x}{40}$

Step 4

Replace all occurrences of $x$ with $3$ in each equation.

Replace all occurrences of $x$ in $y = - \frac{301}{40} + \frac{7 x}{40}$ with $3$ .

$y = - \frac{301}{40} + \frac{7 (3)}{40}$

$x = 3$

Simplify the right side.

Simplify $- \frac{301}{40} + \frac{7 (3)}{40}$ .

Combine the numerators over the common denominator.

$y = \frac{- 301 + 7 (3)}{40}$

$x = 3$

Simplify the expression.

Multiply $7$ by $3$ .

$y = \frac{- 301 + 21}{40}$

$x = 3$

Add $- 301$ and $21$ .

$y = \frac{- 280}{40}$

$x = 3$

Divide $- 280$ by $40$ .

$y = - 7$

$x = 3$

$y = - 7$

$x = 3$

$y = - 7$

$x = 3$

$y = - 7$

$x = 3$

$y = - 7$

$x = 3$

Step 5

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

$(3, - 7)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(3, - 7)$

Equation Form:

$x = 3, y = - 7$

Step 7

Solve the System of Equations -10/3x+1/8y=-87/8 7/10x-4y=301/10

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