Solve by Substitution 6x+6y=-6 , 5x+y=-13

$6 x + 6 y = - 6$ , $5 x + y = - 13$

Step 1

Subtract $5 x$ from both sides of the equation.

$y = - 13 - 5 x$

$6 x + 6 y = - 6$

Step 2

Replace all occurrences of $y$ with $- 13 - 5 x$ in each equation.

Replace all occurrences of $y$ in $6 x + 6 y = - 6$ with $- 13 - 5 x$ .

$6 x + 6 (- 13 - 5 x) = - 6$

$y = - 13 - 5 x$

Simplify the left side.

Simplify $6 x + 6 (- 13 - 5 x)$ .

Simplify each term.

Apply the distributive property.

$6 x + 6 \cdot - 13 + 6 (- 5 x) = - 6$

$y = - 13 - 5 x$

Multiply $6$ by $- 13$ .

$6 x - 78 + 6 (- 5 x) = - 6$

$y = - 13 - 5 x$

Multiply $- 5$ by $6$ .

$6 x - 78 - 30 x = - 6$

$y = - 13 - 5 x$

$6 x - 78 - 30 x = - 6$

$y = - 13 - 5 x$

Subtract $30 x$ from $6 x$ .

$- 24 x - 78 = - 6$

$y = - 13 - 5 x$

$- 24 x - 78 = - 6$

$y = - 13 - 5 x$

$- 24 x - 78 = - 6$

$y = - 13 - 5 x$

$- 24 x - 78 = - 6$

$y = - 13 - 5 x$

Step 3

Solve for $x$ in $- 24 x - 78 = - 6$ .

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

Add $78$ to both sides of the equation.

$- 24 x = - 6 + 78$

$y = - 13 - 5 x$

Add $- 6$ and $78$ .

$- 24 x = 72$

$y = - 13 - 5 x$

$- 24 x = 72$

$y = - 13 - 5 x$

Divide each term in $- 24 x = 72$ by $- 24$ and simplify.

Divide each term in $- 24 x = 72$ by $- 24$ .

$\frac{- 24 x}{- 24} = \frac{72}{- 24}$

$y = - 13 - 5 x$

Simplify the left side.

Cancel the common factor of $- 24$ .

Cancel the common factor.

$\frac{- 24 x}{- 24} = \frac{72}{- 24}$

$y = - 13 - 5 x$

Divide $x$ by $1$ .

$x = \frac{72}{- 24}$

$y = - 13 - 5 x$

$x = \frac{72}{- 24}$

$y = - 13 - 5 x$

$x = \frac{72}{- 24}$

$y = - 13 - 5 x$

Simplify the right side.

Divide $72$ by $- 24$ .

$x = - 3$

$y = - 13 - 5 x$

$x = - 3$

$y = - 13 - 5 x$

$x = - 3$

$y = - 13 - 5 x$

$x = - 3$

$y = - 13 - 5 x$

Step 4

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

Replace all occurrences of $x$ in $y = - 13 - 5 x$ with $- 3$ .

$y = - 13 - 5 \cdot - 3$

$x = - 3$

Simplify the right side.

Simplify $- 13 - 5 \cdot - 3$ .

Multiply $- 5$ by $- 3$ .

$y = - 13 + 15$

$x = - 3$

Add $- 13$ and $15$ .

$y = 2$

$x = - 3$

$y = 2$

$x = - 3$

$y = 2$

$x = - 3$

$y = 2$

$x = - 3$

Step 5

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

$(- 3, 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 3, 2)$

Equation Form:

$x = - 3, y = 2$

Step 7

Solve by Substitution 6x+6y=-6 , 5x+y=-13

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