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

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

Step 1

Replace all occurrences of $x$ with $y + 6$ in each equation.

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

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

$x = y + 6$

Simplify the right side.

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

Simplify each term.

Apply the distributive property.

$y = - 2 - y - 1 \cdot 6$

$x = y + 6$

Multiply $- 1$ by $6$ .

$y = - 2 - y - 6$

$x = y + 6$

$y = - 2 - y - 6$

$x = y + 6$

Subtract $6$ from $- 2$ .

$y = - y - 8$

$x = y + 6$

$y = - y - 8$

$x = y + 6$

$y = - y - 8$

$x = y + 6$

$y = - y - 8$

$x = y + 6$

Step 2

Solve for $y$ in $y = - y - 8$ .

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

Add $y$ to both sides of the equation.

$y + y = - 8$

$x = y + 6$

Add $y$ and $y$ .

$2 y = - 8$

$x = y + 6$

$2 y = - 8$

$x = y + 6$

Divide each term in $2 y = - 8$ by $2$ and simplify.

Divide each term in $2 y = - 8$ by $2$ .

$\frac{2 y}{2} = \frac{- 8}{2}$

$x = y + 6$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{- 8}{2}$

$x = y + 6$

Divide $y$ by $1$ .

$y = \frac{- 8}{2}$

$x = y + 6$

$y = \frac{- 8}{2}$

$x = y + 6$

$y = \frac{- 8}{2}$

$x = y + 6$

Simplify the right side.

Divide $- 8$ by $2$ .

$y = - 4$

$x = y + 6$

$y = - 4$

$x = y + 6$

$y = - 4$

$x = y + 6$

$y = - 4$

$x = y + 6$

Step 3

Replace all occurrences of $y$ with $- 4$ in each equation.

Replace all occurrences of $y$ in $x = y + 6$ with $- 4$ .

$x = (- 4) + 6$

$y = - 4$

Simplify the right side.

Add $- 4$ and $6$ .

$x = 2$

$y = - 4$

$x = 2$

$y = - 4$

$x = 2$

$y = - 4$

Step 4

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

$(2, - 4)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(2, - 4)$

Equation Form:

$x = 2, y = - 4$

Step 6

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

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