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

$x - y = 11$ $- x + y = - 11$

Step 1

Add $y$ to both sides of the equation.

$x = 11 + y$

$- x + y = - 11$

Step 2

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

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

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

$x = 11 + y$

Simplify the left side.

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

Simplify each term.

Apply the distributive property.

$- 1 \cdot 11 - y + y = - 11$

$x = 11 + y$

Multiply $- 1$ by $11$ .

$- 11 - y + y = - 11$

$x = 11 + y$

$- 11 - y + y = - 11$

$x = 11 + y$

Combine the opposite terms in $- 11 - y + y$ .

Add $- y$ and $y$ .

$- 11 + 0 = - 11$

$x = 11 + y$

Add $- 11$ and $0$ .

$- 11 = - 11$

$x = 11 + y$

$- 11 = - 11$

$x = 11 + y$

$- 11 = - 11$

$x = 11 + y$

$- 11 = - 11$

$x = 11 + y$

$- 11 = - 11$

$x = 11 + y$

Step 3

Remove any equations from the system that are always true.

$x = 11 + y$

Step 4