Algebra Examples

$- 2 x + 2 y = 12$ and $- 2 x + 8 y = - 12$

Step 1

Solve for $x$ in $- 2 x + 2 y = 12$ .

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Step 1.1

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

$- 2 x = 12 - 2 y$

$- 2 x + 8 y = - 12$

Step 1.2

Divide each term in $- 2 x = 12 - 2 y$ by $- 2$ and simplify.

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Step 1.2.1

Divide each term in $- 2 x = 12 - 2 y$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{12}{- 2} + \frac{- 2 y}{- 2}$

$- 2 x + 8 y = - 12$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 2$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{12}{- 2} + \frac{- 2 y}{- 2}$

$- 2 x + 8 y = - 12$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{12}{- 2} + \frac{- 2 y}{- 2}$

$- 2 x + 8 y = - 12$

$x = \frac{12}{- 2} + \frac{- 2 y}{- 2}$

$- 2 x + 8 y = - 12$

$x = \frac{12}{- 2} + \frac{- 2 y}{- 2}$

$- 2 x + 8 y = - 12$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Divide $12$ by $- 2$ .

$x = - 6 + \frac{- 2 y}{- 2}$

$- 2 x + 8 y = - 12$

Step 1.2.3.1.2

Cancel the common factor of $- 2$ .

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Step 1.2.3.1.2.1

Cancel the common factor.

$x = - 6 + \frac{- 2 y}{- 2}$

$- 2 x + 8 y = - 12$

Step 1.2.3.1.2.2

Divide $y$ by $1$ .

$x = - 6 + y$

$- 2 x + 8 y = - 12$

$x = - 6 + y$

$- 2 x + 8 y = - 12$

$x = - 6 + y$

$- 2 x + 8 y = - 12$

$x = - 6 + y$

$- 2 x + 8 y = - 12$

$x = - 6 + y$

$- 2 x + 8 y = - 12$

$x = - 6 + y$

$- 2 x + 8 y = - 12$

Step 2

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

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Step 2.1

Replace all occurrences of $x$ in $- 2 x + 8 y = - 12$ with $- 6 + y$ .

$- 2 (- 6 + y) + 8 y = - 12$

$x = - 6 + y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 2 (- 6 + y) + 8 y$ .

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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.

$- 2 \cdot - 6 - 2 y + 8 y = - 12$

$x = - 6 + y$

Step 2.2.1.1.2

Multiply $- 2$ by $- 6$ .

$12 - 2 y + 8 y = - 12$

$x = - 6 + y$

$12 - 2 y + 8 y = - 12$

$x = - 6 + y$

Step 2.2.1.2

Add $- 2 y$ and $8 y$ .

$12 + 6 y = - 12$

$x = - 6 + y$

$12 + 6 y = - 12$

$x = - 6 + y$

$12 + 6 y = - 12$

$x = - 6 + y$

$12 + 6 y = - 12$

$x = - 6 + y$

Step 3

Solve for $y$ in $12 + 6 y = - 12$ .

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Step 3.1

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

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Step 3.1.1

Subtract $12$ from both sides of the equation.

$6 y = - 12 - 12$

$x = - 6 + y$

Step 3.1.2

Subtract $12$ from $- 12$ .

$6 y = - 24$

$x = - 6 + y$

$6 y = - 24$

$x = - 6 + y$

Step 3.2

Divide each term in $6 y = - 24$ by $6$ and simplify.

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Step 3.2.1

Divide each term in $6 y = - 24$ by $6$ .

$\frac{6 y}{6} = \frac{- 24}{6}$

$x = - 6 + y$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $6$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{6 y}{6} = \frac{- 24}{6}$

$x = - 6 + y$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 24}{6}$

$x = - 6 + y$

$y = \frac{- 24}{6}$

$x = - 6 + y$

$y = \frac{- 24}{6}$

$x = - 6 + y$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $- 24$ by $6$ .

$y = - 4$

$x = - 6 + y$

$y = - 4$

$x = - 6 + y$

$y = - 4$

$x = - 6 + y$

$y = - 4$

$x = - 6 + y$

Step 4

Replace all occurrences of $y$ with $- 4$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = - 6 + y$ with $- 4$ .

$x = - 6 - 4$

$y = - 4$

Step 4.2

Simplify $x = - 6 - 4$ .

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Step 4.2.1

Simplify the left side.

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Step 4.2.1.1

Remove parentheses.

$x = - 6 - 4$

$y = - 4$

$x = - 6 - 4$

$y = - 4$

Step 4.2.2

Simplify the right side.

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Step 4.2.2.1

Subtract $4$ from $- 6$ .

$x = - 10$

$y = - 4$

$x = - 10$

$y = - 4$

$x = - 10$

$y = - 4$

$x = - 10$

$y = - 4$

Step 5

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

$(- 10, - 4)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 10, - 4)$

Equation Form:

$x = - 10, y = - 4$

Step 7