Algebra Examples

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

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.

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Step 2.1

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

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

$x = 11 + y$

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

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

$x = 11 + y$

Step 2.2.1.1.2

Multiply $- 1$ by $11$ .

$- 11 - y + y = - 11$

$x = 11 + y$

$- 11 - y + y = - 11$

$x = 11 + y$

Step 2.2.1.2

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

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Step 2.2.1.2.1

Add $- y$ and $y$ .

$- 11 + 0 = - 11$

$x = 11 + y$

Step 2.2.1.2.2

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