Solve by Substitution y-x=9 10+2x=-2y

$y - x = 9$ $10 + 2 x = - 2 y$

Step 1

Add $x$ to both sides of the equation.

$y = 9 + x$

$10 + 2 x = - 2 y$

Step 2

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

Replace all occurrences of $y$ in $10 + 2 x = - 2 y$ with $9 + x$ .

$10 + 2 x = - 2 (9 + x)$

$y = 9 + x$

Simplify the right side.

Simplify $- 2 (9 + x)$ .

Apply the distributive property.

$10 + 2 x = - 2 \cdot 9 - 2 x$

$y = 9 + x$

Multiply $- 2$ by $9$ .

$10 + 2 x = - 18 - 2 x$

$y = 9 + x$

$10 + 2 x = - 18 - 2 x$

$y = 9 + x$

$10 + 2 x = - 18 - 2 x$

$y = 9 + x$

$10 + 2 x = - 18 - 2 x$

$y = 9 + x$

Step 3

Solve for $x$ in $10 + 2 x = - 18 - 2 x$ .

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

Add $2 x$ to both sides of the equation.

$10 + 2 x + 2 x = - 18$

$y = 9 + x$

Add $2 x$ and $2 x$ .

$10 + 4 x = - 18$

$y = 9 + x$

$10 + 4 x = - 18$

$y = 9 + x$

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

Subtract $10$ from both sides of the equation.

$4 x = - 18 - 10$

$y = 9 + x$

Subtract $10$ from $- 18$ .

$4 x = - 28$

$y = 9 + x$

$4 x = - 28$

$y = 9 + x$

Divide each term in $4 x = - 28$ by $4$ and simplify.

Divide each term in $4 x = - 28$ by $4$ .

$\frac{4 x}{4} = \frac{- 28}{4}$

$y = 9 + x$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 28}{4}$

$y = 9 + x$

Divide $x$ by $1$ .

$x = \frac{- 28}{4}$

$y = 9 + x$

$x = \frac{- 28}{4}$

$y = 9 + x$

$x = \frac{- 28}{4}$

$y = 9 + x$

Simplify the right side.

Divide $- 28$ by $4$ .

$x = - 7$

$y = 9 + x$

$x = - 7$

$y = 9 + x$

$x = - 7$

$y = 9 + x$

$x = - 7$

$y = 9 + x$

Step 4

Replace all occurrences of $x$ with $- 7$ in each equation.

Replace all occurrences of $x$ in $y = 9 + x$ with $- 7$ .

$y = 9 - 7$

$x = - 7$

Simplify $y = 9 - 7$ .

Simplify the left side.

Remove parentheses.

$y = 9 - 7$

$x = - 7$

$y = 9 - 7$

$x = - 7$

Simplify the right side.

Subtract $7$ from $9$ .

$y = 2$

$x = - 7$

$y = 2$

$x = - 7$

$y = 2$

$x = - 7$

$y = 2$

$x = - 7$

Step 5

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

$(- 7, 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 7, 2)$

Equation Form:

$x = - 7, y = 2$

Step 7

Solve by Substitution y-x=9 10+2x=-2y

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