Solve the System of Equations x-y=-11 y+7=-2x

$x - y = - 11$ $y + 7 = - 2 x$

Step 1

Add $y$ to both sides of the equation.

$x = - 11 + y$

$y + 7 = - 2 x$

Step 2

Replace all occurrences of $x$ with $- 11 + y$ in each equation.

Replace all occurrences of $x$ in $y + 7 = - 2 x$ with $- 11 + y$ .

$y + 7 = - 2 (- 11 + y)$

$x = - 11 + y$

Simplify the right side.

Simplify $- 2 (- 11 + y)$ .

Apply the distributive property.

$y + 7 = - 2 \cdot - 11 - 2 y$

$x = - 11 + y$

Multiply $- 2$ by $- 11$ .

$y + 7 = 22 - 2 y$

$x = - 11 + y$

$y + 7 = 22 - 2 y$

$x = - 11 + y$

$y + 7 = 22 - 2 y$

$x = - 11 + y$

$y + 7 = 22 - 2 y$

$x = - 11 + y$

Step 3

Solve for $y$ in $y + 7 = 22 - 2 y$ .

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

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

$y + 7 + 2 y = 22$

$x = - 11 + y$

Add $y$ and $2 y$ .

$3 y + 7 = 22$

$x = - 11 + y$

$3 y + 7 = 22$

$x = - 11 + y$

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

Subtract $7$ from both sides of the equation.

$3 y = 22 - 7$

$x = - 11 + y$

Subtract $7$ from $22$ .

$3 y = 15$

$x = - 11 + y$

$3 y = 15$

$x = - 11 + y$

Divide each term in $3 y = 15$ by $3$ and simplify.

Divide each term in $3 y = 15$ by $3$ .

$\frac{3 y}{3} = \frac{15}{3}$

$x = - 11 + y$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{15}{3}$

$x = - 11 + y$

Divide $y$ by $1$ .

$y = \frac{15}{3}$

$x = - 11 + y$

$y = \frac{15}{3}$

$x = - 11 + y$

$y = \frac{15}{3}$

$x = - 11 + y$

Simplify the right side.

Divide $15$ by $3$ .

$y = 5$

$x = - 11 + y$

$y = 5$

$x = - 11 + y$

$y = 5$

$x = - 11 + y$

$y = 5$

$x = - 11 + y$

Step 4

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

Replace all occurrences of $y$ in $x = - 11 + y$ with $5$ .

$x = - 11 + 5$

$y = 5$

Simplify $x = - 11 + 5$ .

Simplify the left side.

Remove parentheses.

$x = - 11 + 5$

$y = 5$

$x = - 11 + 5$

$y = 5$

Simplify the right side.

Add $- 11$ and $5$ .

$x = - 6$

$y = 5$

$x = - 6$

$y = 5$

$x = - 6$

$y = 5$

$x = - 6$

$y = 5$

Step 5

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

$(- 6, 5)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 6, 5)$

Equation Form:

$x = - 6, y = 5$

Step 7

Solve the System of Equations x-y=-11 y+7=-2x

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