Solve by Substitution -4x-15y=-17 , -x+5y=-13

$- 4 x - 15 y = - 17$ , $- x + 5 y = - 13$

Step 1

Solve for $x$ in $- 4 x - 15 y = - 17$ .

Add $15 y$ to both sides of the equation.

$- 4 x = - 17 + 15 y$

$- x + 5 y = - 13$

Divide each term in $- 4 x = - 17 + 15 y$ by $- 4$ and simplify.

Divide each term in $- 4 x = - 17 + 15 y$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 17}{- 4} + \frac{15 y}{- 4}$

$- x + 5 y = - 13$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 17}{- 4} + \frac{15 y}{- 4}$

$- x + 5 y = - 13$

Divide $x$ by $1$ .

$x = \frac{- 17}{- 4} + \frac{15 y}{- 4}$

$- x + 5 y = - 13$

$x = \frac{- 17}{- 4} + \frac{15 y}{- 4}$

$- x + 5 y = - 13$

$x = \frac{- 17}{- 4} + \frac{15 y}{- 4}$

$- x + 5 y = - 13$

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

$x = \frac{17}{4} + \frac{15 y}{- 4}$

$- x + 5 y = - 13$

Move the negative in front of the fraction.

$x = \frac{17}{4} - \frac{15 y}{4}$

$- x + 5 y = - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

$- x + 5 y = - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

$- x + 5 y = - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

$- x + 5 y = - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

$- x + 5 y = - 13$

Step 2

Replace all occurrences of $x$ with $\frac{17}{4} - \frac{15 y}{4}$ in each equation.

Replace all occurrences of $x$ in $- x + 5 y = - 13$ with $\frac{17}{4} - \frac{15 y}{4}$ .

$- (\frac{17}{4} - \frac{15 y}{4}) + 5 y = - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

Simplify the left side.

Simplify $- (\frac{17}{4} - \frac{15 y}{4}) + 5 y$ .

Simplify each term.

Apply the distributive property.

$- \frac{17}{4} + \frac{15 y}{4} + 5 y = - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

Multiply $- - \frac{15 y}{4}$ .

Multiply $- 1$ by $- 1$ .

$- \frac{17}{4} + 1 (\frac{15 y}{4}) + 5 y = - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

Multiply $\frac{15 y}{4}$ by $1$ .

$- \frac{17}{4} + \frac{15 y}{4} + 5 y = - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

$- \frac{17}{4} + \frac{15 y}{4} + 5 y = - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

$- \frac{17}{4} + \frac{15 y}{4} + 5 y = - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

To write $5 y$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{17}{4} + \frac{15 y}{4} + 5 y \cdot \frac{4}{4} = - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

Combine $5 y$ and $\frac{4}{4}$ .

$- \frac{17}{4} + \frac{15 y}{4} + \frac{5 y \cdot 4}{4} = - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

Combine the numerators over the common denominator.

$- \frac{17}{4} + \frac{15 y + 5 y \cdot 4}{4} = - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

Combine the numerators over the common denominator.

$\frac{- 17 + 15 y + 5 y \cdot 4}{4} = - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

Multiply $4$ by $5$ .

$\frac{- 17 + 15 y + 20 y}{4} = - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

Add $15 y$ and $20 y$ .

$\frac{- 17 + 35 y}{4} = - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

Rewrite $- 17$ as $- 1 (17)$ .

$\frac{- 1 \cdot 17 + 35 y}{4} = - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

Factor $- 1$ out of $35 y$ .

$\frac{- 1 \cdot 17 - (- 35 y)}{4} = - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

Factor $- 1$ out of $- 1 (17) - (- 35 y)$ .

$\frac{- 1 (17 - 35 y)}{4} = - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

Move the negative in front of the fraction.

$- \frac{17 - 35 y}{4} = - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

$- \frac{17 - 35 y}{4} = - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

$- \frac{17 - 35 y}{4} = - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

$- \frac{17 - 35 y}{4} = - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

Step 3

Solve for $y$ in $- \frac{17 - 35 y}{4} = - 13$ .

Multiply both sides of the equation by $- 4$ .

$- 4 (- \frac{17 - 35 y}{4}) = - 4 \cdot - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 4 (- \frac{17 - 35 y}{4})$ .

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{17 - 35 y}{4}$ into the numerator.

$- 4 \frac{- (17 - 35 y)}{4} = - 4 \cdot - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

Factor $4$ out of $- 4$ .

$4 (- 1) (\frac{- (17 - 35 y)}{4}) = - 4 \cdot - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

Cancel the common factor.

$4 \cdot (- 1 \frac{- (17 - 35 y)}{4}) = - 4 \cdot - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

Rewrite the expression.

$17 - 35 y = - 4 \cdot - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

$17 - 35 y = - 4 \cdot - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (17 - 35 y) = - 4 \cdot - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

Multiply $17 - 35 y$ by $1$ .

$17 - 35 y = - 4 \cdot - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

$17 - 35 y = - 4 \cdot - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

$17 - 35 y = - 4 \cdot - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

$17 - 35 y = - 4 \cdot - 13$

$x = \frac{17}{4} - \frac{15 y}{4}$

Simplify the right side.

Multiply $- 4$ by $- 13$ .

$17 - 35 y = 52$

$x = \frac{17}{4} - \frac{15 y}{4}$

$17 - 35 y = 52$

$x = \frac{17}{4} - \frac{15 y}{4}$

$17 - 35 y = 52$

$x = \frac{17}{4} - \frac{15 y}{4}$

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

Subtract $17$ from both sides of the equation.

$- 35 y = 52 - 17$

$x = \frac{17}{4} - \frac{15 y}{4}$

Subtract $17$ from $52$ .

$- 35 y = 35$

$x = \frac{17}{4} - \frac{15 y}{4}$

$- 35 y = 35$

$x = \frac{17}{4} - \frac{15 y}{4}$

Divide each term in $- 35 y = 35$ by $- 35$ and simplify.

Divide each term in $- 35 y = 35$ by $- 35$ .

$\frac{- 35 y}{- 35} = \frac{35}{- 35}$

$x = \frac{17}{4} - \frac{15 y}{4}$

Simplify the left side.

Cancel the common factor of $- 35$ .

Cancel the common factor.

$\frac{- 35 y}{- 35} = \frac{35}{- 35}$

$x = \frac{17}{4} - \frac{15 y}{4}$

Divide $y$ by $1$ .

$y = \frac{35}{- 35}$

$x = \frac{17}{4} - \frac{15 y}{4}$

$y = \frac{35}{- 35}$

$x = \frac{17}{4} - \frac{15 y}{4}$

$y = \frac{35}{- 35}$

$x = \frac{17}{4} - \frac{15 y}{4}$

Simplify the right side.

Divide $35$ by $- 35$ .

$y = - 1$

$x = \frac{17}{4} - \frac{15 y}{4}$

$y = - 1$

$x = \frac{17}{4} - \frac{15 y}{4}$

$y = - 1$

$x = \frac{17}{4} - \frac{15 y}{4}$

$y = - 1$

$x = \frac{17}{4} - \frac{15 y}{4}$

Step 4

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

Replace all occurrences of $y$ in $x = \frac{17}{4} - \frac{15 y}{4}$ with $- 1$ .

$x = \frac{17}{4} - \frac{15 (- 1)}{4}$

$y = - 1$

Simplify the right side.

Simplify $\frac{17}{4} - \frac{15 (- 1)}{4}$ .

Combine the numerators over the common denominator.

$x = \frac{17 - 15 \cdot - 1}{4}$

$y = - 1$

Simplify the expression.

Multiply $- 15$ by $- 1$ .

$x = \frac{17 + 15}{4}$

$y = - 1$

Add $17$ and $15$ .

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

$y = - 1$

Divide $32$ by $4$ .

$x = 8$

$y = - 1$

$x = 8$

$y = - 1$

$x = 8$

$y = - 1$

$x = 8$

$y = - 1$

$x = 8$

$y = - 1$

Step 5

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

$(8, - 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(8, - 1)$

Equation Form:

$x = 8, y = - 1$

Step 7

Solve by Substitution -4x-15y=-17 , -x+5y=-13

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