Solve by Substitution -5x-8y=17 , 2x-7y=-17

$- 5 x - 8 y = 17$ , $2 x - 7 y = - 17$

Step 1

Solve for $x$ in $- 5 x - 8 y = 17$ .

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

$- 5 x = 17 + 8 y$

$2 x - 7 y = - 17$

Divide each term in $- 5 x = 17 + 8 y$ by $- 5$ and simplify.

Divide each term in $- 5 x = 17 + 8 y$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{17}{- 5} + \frac{8 y}{- 5}$

$2 x - 7 y = - 17$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{17}{- 5} + \frac{8 y}{- 5}$

$2 x - 7 y = - 17$

Divide $x$ by $1$ .

$x = \frac{17}{- 5} + \frac{8 y}{- 5}$

$2 x - 7 y = - 17$

$x = \frac{17}{- 5} + \frac{8 y}{- 5}$

$2 x - 7 y = - 17$

$x = \frac{17}{- 5} + \frac{8 y}{- 5}$

$2 x - 7 y = - 17$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{17}{5} + \frac{8 y}{- 5}$

$2 x - 7 y = - 17$

Move the negative in front of the fraction.

$x = - \frac{17}{5} - \frac{8 y}{5}$

$2 x - 7 y = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

$2 x - 7 y = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

$2 x - 7 y = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

$2 x - 7 y = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

$2 x - 7 y = - 17$

Step 2

Replace all occurrences of $x$ with $- \frac{17}{5} - \frac{8 y}{5}$ in each equation.

Replace all occurrences of $x$ in $2 x - 7 y = - 17$ with $- \frac{17}{5} - \frac{8 y}{5}$ .

$2 (- \frac{17}{5} - \frac{8 y}{5}) - 7 y = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Simplify the left side.

Simplify $2 (- \frac{17}{5} - \frac{8 y}{5}) - 7 y$ .

Simplify each term.

Apply the distributive property.

$2 (- \frac{17}{5}) + 2 (- \frac{8 y}{5}) - 7 y = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Multiply $2 (- \frac{17}{5})$ .

Multiply $- 1$ by $2$ .

$- 2 (\frac{17}{5}) + 2 (- \frac{8 y}{5}) - 7 y = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Combine $- 2$ and $\frac{17}{5}$ .

$\frac{- 2 \cdot 17}{5} + 2 (- \frac{8 y}{5}) - 7 y = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Multiply $- 2$ by $17$ .

$\frac{- 34}{5} + 2 (- \frac{8 y}{5}) - 7 y = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

$\frac{- 34}{5} + 2 (- \frac{8 y}{5}) - 7 y = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Multiply $2 (- \frac{8 y}{5})$ .

Multiply $- 1$ by $2$ .

$\frac{- 34}{5} - 2 \frac{8 y}{5} - 7 y = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Combine $- 2$ and $\frac{8 y}{5}$ .

$\frac{- 34}{5} + \frac{- 2 (8 y)}{5} - 7 y = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Multiply $8$ by $- 2$ .

$\frac{- 34}{5} + \frac{- 16 y}{5} - 7 y = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

$\frac{- 34}{5} + \frac{- 16 y}{5} - 7 y = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Simplify each term.

Move the negative in front of the fraction.

$- \frac{34}{5} + \frac{- 16 y}{5} - 7 y = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Move the negative in front of the fraction.

$- \frac{34}{5} - \frac{16 y}{5} - 7 y = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

$- \frac{34}{5} - \frac{16 y}{5} - 7 y = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

$- \frac{34}{5} - \frac{16 y}{5} - 7 y = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

To write $- 7 y$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{34}{5} - \frac{16 y}{5} - 7 y \cdot \frac{5}{5} = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Combine $- 7 y$ and $\frac{5}{5}$ .

$- \frac{34}{5} - \frac{16 y}{5} + \frac{- 7 y \cdot 5}{5} = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Combine the numerators over the common denominator.

$- \frac{34}{5} + \frac{- 16 y - 7 y \cdot 5}{5} = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Combine the numerators over the common denominator.

$\frac{- 34 - 16 y - 7 y \cdot 5}{5} = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Multiply $5$ by $- 7$ .

$\frac{- 34 - 16 y - 35 y}{5} = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Subtract $35 y$ from $- 16 y$ .

$\frac{- 34 - 51 y}{5} = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Factor $17$ out of $- 34 - 51 y$ .

Factor $17$ out of $- 34$ .

$\frac{17 (- 2) - 51 y}{5} = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Factor $17$ out of $- 51 y$ .

$\frac{17 (- 2) + 17 (- 3 y)}{5} = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Factor $17$ out of $17 (- 2) + 17 (- 3 y)$ .

$\frac{17 (- 2 - 3 y)}{5} = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

$\frac{17 (- 2 - 3 y)}{5} = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Rewrite $- 2$ as $- 1 (2)$ .

$\frac{17 (- 1 \cdot 2 - 3 y)}{5} = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Factor $- 1$ out of $- 3 y$ .

$\frac{17 (- 1 \cdot 2 - (3 y))}{5} = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Factor $- 1$ out of $- 1 (2) - (3 y)$ .

$\frac{17 (- 1 (2 + 3 y))}{5} = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Move the negative in front of the fraction.

$- \frac{17 (2 + 3 y)}{5} = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

$- \frac{17 (2 + 3 y)}{5} = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

$- \frac{17 (2 + 3 y)}{5} = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

$- \frac{17 (2 + 3 y)}{5} = - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Step 3

Solve for $y$ in $- \frac{17 (2 + 3 y)}{5} = - 17$ .

Multiply both sides of the equation by $- \frac{5}{17}$ .

$- \frac{5}{17} \cdot (- \frac{17 (2 + 3 y)}{5}) = - \frac{5}{17} \cdot - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{5}{17} (- \frac{17 (2 + 3 y)}{5})$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{5}{17}$ into the numerator.

$\frac{- 5}{17} \cdot (- \frac{17 (2 + 3 y)}{5}) = - \frac{5}{17} \cdot - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Move the leading negative in $- \frac{17 (2 + 3 y)}{5}$ into the numerator.

$\frac{- 5}{17} \cdot \frac{- 17 (2 + 3 y)}{5} = - \frac{5}{17} \cdot - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{17} \cdot \frac{- 17 (2 + 3 y)}{5} = - \frac{5}{17} \cdot - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Cancel the common factor.

$\frac{5 \cdot - 1}{17} \cdot \frac{- 17 (2 + 3 y)}{5} = - \frac{5}{17} \cdot - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Rewrite the expression.

$\frac{- 1}{17} \cdot (- 17 (2 + 3 y)) = - \frac{5}{17} \cdot - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

$\frac{- 1}{17} \cdot (- 17 (2 + 3 y)) = - \frac{5}{17} \cdot - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Cancel the common factor of $17$ .

Factor $17$ out of $- 17 (2 + 3 y)$ .

$\frac{- 1}{17} \cdot (17 (- (2 + 3 y))) = - \frac{5}{17} \cdot - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Cancel the common factor.

$\frac{- 1}{17} \cdot (17 (- (2 + 3 y))) = - \frac{5}{17} \cdot - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Rewrite the expression.

$2 + 3 y = - \frac{5}{17} \cdot - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

$2 + 3 y = - \frac{5}{17} \cdot - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (2 + 3 y) = - \frac{5}{17} \cdot - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Multiply $2 + 3 y$ by $1$ .

$2 + 3 y = - \frac{5}{17} \cdot - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

$2 + 3 y = - \frac{5}{17} \cdot - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

$2 + 3 y = - \frac{5}{17} \cdot - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

$2 + 3 y = - \frac{5}{17} \cdot - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Simplify the right side.

Simplify $- \frac{5}{17} \cdot - 17$ .

Cancel the common factor of $17$ .

Move the leading negative in $- \frac{5}{17}$ into the numerator.

$2 + 3 y = \frac{- 5}{17} \cdot - 17$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Factor $17$ out of $- 17$ .

$2 + 3 y = \frac{- 5}{17} \cdot (17 (- 1))$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Cancel the common factor.

$2 + 3 y = \frac{- 5}{17} \cdot (17 \cdot - 1)$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Rewrite the expression.

$2 + 3 y = - 5 \cdot - 1$

$x = - \frac{17}{5} - \frac{8 y}{5}$

$2 + 3 y = - 5 \cdot - 1$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Multiply $- 5$ by $- 1$ .

$2 + 3 y = 5$

$x = - \frac{17}{5} - \frac{8 y}{5}$

$2 + 3 y = 5$

$x = - \frac{17}{5} - \frac{8 y}{5}$

$2 + 3 y = 5$

$x = - \frac{17}{5} - \frac{8 y}{5}$

$2 + 3 y = 5$

$x = - \frac{17}{5} - \frac{8 y}{5}$

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

Subtract $2$ from both sides of the equation.

$3 y = 5 - 2$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Subtract $2$ from $5$ .

$3 y = 3$

$x = - \frac{17}{5} - \frac{8 y}{5}$

$3 y = 3$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Divide each term in $3 y = 3$ by $3$ and simplify.

Divide each term in $3 y = 3$ by $3$ .

$\frac{3 y}{3} = \frac{3}{3}$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{3}{3}$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Divide $y$ by $1$ .

$y = \frac{3}{3}$

$x = - \frac{17}{5} - \frac{8 y}{5}$

$y = \frac{3}{3}$

$x = - \frac{17}{5} - \frac{8 y}{5}$

$y = \frac{3}{3}$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Simplify the right side.

Divide $3$ by $3$ .

$y = 1$

$x = - \frac{17}{5} - \frac{8 y}{5}$

$y = 1$

$x = - \frac{17}{5} - \frac{8 y}{5}$

$y = 1$

$x = - \frac{17}{5} - \frac{8 y}{5}$

$y = 1$

$x = - \frac{17}{5} - \frac{8 y}{5}$

Step 4

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

Replace all occurrences of $y$ in $x = - \frac{17}{5} - \frac{8 y}{5}$ with $1$ .

$x = - \frac{17}{5} - \frac{8 (1)}{5}$

$y = 1$

Simplify the right side.

Simplify $- \frac{17}{5} - \frac{8 (1)}{5}$ .

Combine the numerators over the common denominator.

$x = \frac{- 17 - 8 \cdot 1}{5}$

$y = 1$

Simplify the expression.

Multiply $- 8$ by $1$ .

$x = \frac{- 17 - 8}{5}$

$y = 1$

Subtract $8$ from $- 17$ .

$x = \frac{- 25}{5}$

$y = 1$

Divide $- 25$ by $5$ .

$x = - 5$

$y = 1$

$x = - 5$

$y = 1$

$x = - 5$

$y = 1$

$x = - 5$

$y = 1$

$x = - 5$

$y = 1$

Step 5

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

$(- 5, 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 5, 1)$

Equation Form:

$x = - 5, y = 1$

Step 7

Solve by Substitution -5x-8y=17 , 2x-7y=-17

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