Algebra Examples

$x + 2 y = 6$ $- x - 2 y + 6 = 0$

Step 1

Subtract $2 y$ from both sides of the equation.

$x = 6 - 2 y$

$- x - 2 y + 6 = 0$

Step 2

Replace all occurrences of $x$ with $6 - 2 y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $- x - 2 y + 6 = 0$ with $6 - 2 y$ .

$- (6 - 2 y) - 2 y + 6 = 0$

$x = 6 - 2 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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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.

$- 1 \cdot 6 - (- 2 y) - 2 y + 6 = 0$

$x = 6 - 2 y$

Step 2.2.1.1.2

Multiply $- 1$ by $6$ .

$- 6 - (- 2 y) - 2 y + 6 = 0$

$x = 6 - 2 y$

Step 2.2.1.1.3

Multiply $- 2$ by $- 1$ .

$- 6 + 2 y - 2 y + 6 = 0$

$x = 6 - 2 y$

$- 6 + 2 y - 2 y + 6 = 0$

$x = 6 - 2 y$

Step 2.2.1.2

Combine the opposite terms in $- 6 + 2 y - 2 y + 6$ .

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Step 2.2.1.2.1

Subtract $2 y$ from $2 y$ .

$- 6 + 0 + 6 = 0$

$x = 6 - 2 y$

Step 2.2.1.2.2

Add $- 6$ and $0$ .

$- 6 + 6 = 0$

$x = 6 - 2 y$

Step 2.2.1.2.3

Add $- 6$ and $6$ .

$0 = 0$

$x = 6 - 2 y$

$0 = 0$

$x = 6 - 2 y$

$0 = 0$

$x = 6 - 2 y$

$0 = 0$

$x = 6 - 2 y$

$0 = 0$

$x = 6 - 2 y$

Step 3

Remove any equations from the system that are always true.

$x = 6 - 2 y$

Step 4