Solve the System of Equations 7y+13=-5x 5x=8y-28

$7 y + 13 = - 5 x$ $5 x = 8 y - 28$

Step 1

Divide each term in $5 x = 8 y - 28$ by $5$ and simplify.

Divide each term in $5 x = 8 y - 28$ by $5$ .

$\frac{5 x}{5} = \frac{8 y}{5} + \frac{- 28}{5}$

$7 y + 13 = - 5 x$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{8 y}{5} + \frac{- 28}{5}$

$7 y + 13 = - 5 x$

Divide $x$ by $1$ .

$x = \frac{8 y}{5} + \frac{- 28}{5}$

$7 y + 13 = - 5 x$

$x = \frac{8 y}{5} + \frac{- 28}{5}$

$7 y + 13 = - 5 x$

$x = \frac{8 y}{5} + \frac{- 28}{5}$

$7 y + 13 = - 5 x$

Simplify the right side.

Move the negative in front of the fraction.

$x = \frac{8 y}{5} - \frac{28}{5}$

$7 y + 13 = - 5 x$

$x = \frac{8 y}{5} - \frac{28}{5}$

$7 y + 13 = - 5 x$

$x = \frac{8 y}{5} - \frac{28}{5}$

$7 y + 13 = - 5 x$

Step 2

Replace all occurrences of $x$ with $\frac{8 y}{5} - \frac{28}{5}$ in each equation.

Replace all occurrences of $x$ in $7 y + 13 = - 5 x$ with $\frac{8 y}{5} - \frac{28}{5}$ .

$7 y + 13 = - 5 (\frac{8 y}{5} - \frac{28}{5})$

$x = \frac{8 y}{5} - \frac{28}{5}$

Simplify the right side.

Simplify $- 5 (\frac{8 y}{5} - \frac{28}{5})$ .

Apply the distributive property.

$7 y + 13 = - 5 \frac{8 y}{5} - 5 (- \frac{28}{5})$

$x = \frac{8 y}{5} - \frac{28}{5}$

Cancel the common factor of $5$ .

Factor $5$ out of $- 5$ .

$7 y + 13 = 5 (- 1) (\frac{8 y}{5}) - 5 (- \frac{28}{5})$

$x = \frac{8 y}{5} - \frac{28}{5}$

Cancel the common factor.

$7 y + 13 = 5 \cdot (- 1 \frac{8 y}{5}) - 5 (- \frac{28}{5})$

$x = \frac{8 y}{5} - \frac{28}{5}$

Rewrite the expression.

$7 y + 13 = - 1 (8 y) - 5 (- \frac{28}{5})$

$x = \frac{8 y}{5} - \frac{28}{5}$

$7 y + 13 = - 1 (8 y) - 5 (- \frac{28}{5})$

$x = \frac{8 y}{5} - \frac{28}{5}$

Multiply $8$ by $- 1$ .

$7 y + 13 = - 8 y - 5 (- \frac{28}{5})$

$x = \frac{8 y}{5} - \frac{28}{5}$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{28}{5}$ into the numerator.

$7 y + 13 = - 8 y - 5 (\frac{- 28}{5})$

$x = \frac{8 y}{5} - \frac{28}{5}$

Factor $5$ out of $- 5$ .

$7 y + 13 = - 8 y + 5 (- 1) (\frac{- 28}{5})$

$x = \frac{8 y}{5} - \frac{28}{5}$

Cancel the common factor.

$7 y + 13 = - 8 y + 5 \cdot (- 1 (\frac{- 28}{5}))$

$x = \frac{8 y}{5} - \frac{28}{5}$

Rewrite the expression.

$7 y + 13 = - 8 y - 1 \cdot - 28$

$x = \frac{8 y}{5} - \frac{28}{5}$

$7 y + 13 = - 8 y - 1 \cdot - 28$

$x = \frac{8 y}{5} - \frac{28}{5}$

Multiply $- 1$ by $- 28$ .

$7 y + 13 = - 8 y + 28$

$x = \frac{8 y}{5} - \frac{28}{5}$

$7 y + 13 = - 8 y + 28$

$x = \frac{8 y}{5} - \frac{28}{5}$

$7 y + 13 = - 8 y + 28$

$x = \frac{8 y}{5} - \frac{28}{5}$

$7 y + 13 = - 8 y + 28$

$x = \frac{8 y}{5} - \frac{28}{5}$

Step 3

Solve for $y$ in $7 y + 13 = - 8 y + 28$ .

Move all terms containing $y$ to the left side of the equation.

Add $8 y$ to both sides of the equation.

$7 y + 13 + 8 y = 28$

$x = \frac{8 y}{5} - \frac{28}{5}$

Add $7 y$ and $8 y$ .

$15 y + 13 = 28$

$x = \frac{8 y}{5} - \frac{28}{5}$

$15 y + 13 = 28$

$x = \frac{8 y}{5} - \frac{28}{5}$

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

Subtract $13$ from both sides of the equation.

$15 y = 28 - 13$

$x = \frac{8 y}{5} - \frac{28}{5}$

Subtract $13$ from $28$ .

$15 y = 15$

$x = \frac{8 y}{5} - \frac{28}{5}$

$15 y = 15$

$x = \frac{8 y}{5} - \frac{28}{5}$

Divide each term in $15 y = 15$ by $15$ and simplify.

Divide each term in $15 y = 15$ by $15$ .

$\frac{15 y}{15} = \frac{15}{15}$

$x = \frac{8 y}{5} - \frac{28}{5}$

Simplify the left side.

Cancel the common factor of $15$ .

Cancel the common factor.

$\frac{15 y}{15} = \frac{15}{15}$

$x = \frac{8 y}{5} - \frac{28}{5}$

Divide $y$ by $1$ .

$y = \frac{15}{15}$

$x = \frac{8 y}{5} - \frac{28}{5}$

$y = \frac{15}{15}$

$x = \frac{8 y}{5} - \frac{28}{5}$

$y = \frac{15}{15}$

$x = \frac{8 y}{5} - \frac{28}{5}$

Simplify the right side.

Divide $15$ by $15$ .

$y = 1$

$x = \frac{8 y}{5} - \frac{28}{5}$

$y = 1$

$x = \frac{8 y}{5} - \frac{28}{5}$

$y = 1$

$x = \frac{8 y}{5} - \frac{28}{5}$

$y = 1$

$x = \frac{8 y}{5} - \frac{28}{5}$

Step 4

Replace all occurrences of $y$ with $1$ in each equation.

Replace all occurrences of $y$ in $x = \frac{8 y}{5} - \frac{28}{5}$ with $1$ .

$x = \frac{8 (1)}{5} - \frac{28}{5}$

$y = 1$

Simplify the right side.

Simplify $\frac{8 (1)}{5} - \frac{28}{5}$ .

Combine the numerators over the common denominator.

$x = \frac{8 (1) - 28}{5}$

$y = 1$

Simplify the expression.

Multiply $8$ by $1$ .

$x = \frac{8 - 28}{5}$

$y = 1$

Subtract $28$ from $8$ .

$x = \frac{- 20}{5}$

$y = 1$

Divide $- 20$ by $5$ .

$x = - 4$

$y = 1$

$x = - 4$

$y = 1$

$x = - 4$

$y = 1$

$x = - 4$

$y = 1$

$x = - 4$

$y = 1$

Step 5

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

$(- 4, 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 4, 1)$

Equation Form:

$x = - 4, y = 1$

Step 7

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