Solve by Substitution x+2y=12 -x=-y-6

$x + 2 y = 12$ $- x = - y - 6$

Step 1

Subtract $2 y$ from both sides of the equation.

$x = 12 - 2 y$

$- x = - y - 6$

Step 2

Replace all occurrences of $x$ with $12 - 2 y$ in each equation.

Replace all occurrences of $x$ in $- x = - y - 6$ with $12 - 2 y$ .

$- (12 - 2 y) = - y - 6$

$x = 12 - 2 y$

Simplify the left side.

Simplify $- (12 - 2 y)$ .

Apply the distributive property.

$- 1 \cdot 12 - (- 2 y) = - y - 6$

$x = 12 - 2 y$

Multiply.

Multiply $- 1$ by $12$ .

$- 12 - (- 2 y) = - y - 6$

$x = 12 - 2 y$

Multiply $- 2$ by $- 1$ .

$- 12 + 2 y = - y - 6$

$x = 12 - 2 y$

$- 12 + 2 y = - y - 6$

$x = 12 - 2 y$

$- 12 + 2 y = - y - 6$

$x = 12 - 2 y$

$- 12 + 2 y = - y - 6$

$x = 12 - 2 y$

$- 12 + 2 y = - y - 6$

$x = 12 - 2 y$

Step 3

Solve for $y$ in $- 12 + 2 y = - y - 6$ .

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

Add $y$ to both sides of the equation.

$- 12 + 2 y + y = - 6$

$x = 12 - 2 y$

Add $2 y$ and $y$ .

$- 12 + 3 y = - 6$

$x = 12 - 2 y$

$- 12 + 3 y = - 6$

$x = 12 - 2 y$

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

Add $12$ to both sides of the equation.

$3 y = - 6 + 12$

$x = 12 - 2 y$

Add $- 6$ and $12$ .

$3 y = 6$

$x = 12 - 2 y$

$3 y = 6$

$x = 12 - 2 y$

Divide each term in $3 y = 6$ by $3$ and simplify.

Divide each term in $3 y = 6$ by $3$ .

$\frac{3 y}{3} = \frac{6}{3}$

$x = 12 - 2 y$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{6}{3}$

$x = 12 - 2 y$

Divide $y$ by $1$ .

$y = \frac{6}{3}$

$x = 12 - 2 y$

$y = \frac{6}{3}$

$x = 12 - 2 y$

$y = \frac{6}{3}$

$x = 12 - 2 y$

Simplify the right side.

Divide $6$ by $3$ .

$y = 2$

$x = 12 - 2 y$

$y = 2$

$x = 12 - 2 y$

$y = 2$

$x = 12 - 2 y$

$y = 2$

$x = 12 - 2 y$

Step 4

Replace all occurrences of $y$ with $2$ in each equation.

Replace all occurrences of $y$ in $x = 12 - 2 y$ with $2$ .

$x = 12 - 2 \cdot 2$

$y = 2$

Simplify the right side.

Simplify $12 - 2 \cdot 2$ .

Multiply $- 2$ by $2$ .

$x = 12 - 4$

$y = 2$

Subtract $4$ from $12$ .

$x = 8$

$y = 2$

$x = 8$

$y = 2$

$x = 8$

$y = 2$

$x = 8$

$y = 2$

Step 5

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

$(8, 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(8, 2)$

Equation Form:

$x = 8, y = 2$

Step 7

Solve by Substitution x+2y=12 -x=-y-6

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