Solve the System of Equations 6(x+y)=6 -2x-6y=-38

$6 (x + y) = 6$ $- 2 x - 6 y = - 38$

Step 1

Solve for $x$ in $6 (x + y) = 6$ .

Divide each term in $6 (x + y) = 6$ by $6$ and simplify.

Divide each term in $6 (x + y) = 6$ by $6$ .

$\frac{6 (x + y)}{6} = \frac{6}{6}$

$- 2 x - 6 y = - 38$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 (x + y)}{6} = \frac{6}{6}$

$- 2 x - 6 y = - 38$

Divide $x + y$ by $1$ .

$x + y = \frac{6}{6}$

$- 2 x - 6 y = - 38$

$x + y = \frac{6}{6}$

$- 2 x - 6 y = - 38$

$x + y = \frac{6}{6}$

$- 2 x - 6 y = - 38$

Simplify the right side.

Divide $6$ by $6$ .

$x + y = 1$

$- 2 x - 6 y = - 38$

$x + y = 1$

$- 2 x - 6 y = - 38$

$x + y = 1$

$- 2 x - 6 y = - 38$

Subtract $y$ from both sides of the equation.

$x = 1 - y$

$- 2 x - 6 y = - 38$

$x = 1 - y$

$- 2 x - 6 y = - 38$

Step 2

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

Replace all occurrences of $x$ in $- 2 x - 6 y = - 38$ with $1 - y$ .

$- 2 (1 - y) - 6 y = - 38$

$x = 1 - y$

Simplify the left side.

Simplify $- 2 (1 - y) - 6 y$ .

Simplify each term.

Apply the distributive property.

$- 2 \cdot 1 - 2 (- y) - 6 y = - 38$

$x = 1 - y$

Multiply $- 2$ by $1$ .

$- 2 - 2 (- y) - 6 y = - 38$

$x = 1 - y$

Multiply $- 1$ by $- 2$ .

$- 2 + 2 y - 6 y = - 38$

$x = 1 - y$

$- 2 + 2 y - 6 y = - 38$

$x = 1 - y$

Subtract $6 y$ from $2 y$ .

$- 2 - 4 y = - 38$

$x = 1 - y$

$- 2 - 4 y = - 38$

$x = 1 - y$

$- 2 - 4 y = - 38$

$x = 1 - y$

$- 2 - 4 y = - 38$

$x = 1 - y$

Step 3

Solve for $y$ in $- 2 - 4 y = - 38$ .

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

Add $2$ to both sides of the equation.

$- 4 y = - 38 + 2$

$x = 1 - y$

Add $- 38$ and $2$ .

$- 4 y = - 36$

$x = 1 - y$

$- 4 y = - 36$

$x = 1 - y$

Divide each term in $- 4 y = - 36$ by $- 4$ and simplify.

Divide each term in $- 4 y = - 36$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{- 36}{- 4}$

$x = 1 - y$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{- 36}{- 4}$

$x = 1 - y$

Divide $y$ by $1$ .

$y = \frac{- 36}{- 4}$

$x = 1 - y$

$y = \frac{- 36}{- 4}$

$x = 1 - y$

$y = \frac{- 36}{- 4}$

$x = 1 - y$

Simplify the right side.

Divide $- 36$ by $- 4$ .

$y = 9$

$x = 1 - y$

$y = 9$

$x = 1 - y$

$y = 9$

$x = 1 - y$

$y = 9$

$x = 1 - y$

Step 4

Replace all occurrences of $y$ with $9$ in each equation.

Replace all occurrences of $y$ in $x = 1 - y$ with $9$ .

$x = 1 - (9)$

$y = 9$

Simplify the right side.

Simplify $1 - (9)$ .

Multiply $- 1$ by $9$ .

$x = 1 - 9$

$y = 9$

Subtract $9$ from $1$ .

$x = - 8$

$y = 9$

$x = - 8$

$y = 9$

$x = - 8$

$y = 9$

$x = - 8$

$y = 9$

Step 5

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

$(- 8, 9)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 8, 9)$

Equation Form:

$x = - 8, y = 9$

Step 7

Solve the System of Equations 6(x+y)=6 -2x-6y=-38

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