Algebra Examples

$x - y = - 12$ and $- 8 x - 4 y = - 12$

Step 1

Add $y$ to both sides of the equation.

$x = - 12 + y$

$- 8 x - 4 y = - 12$

Step 2

Replace all occurrences of $x$ with $- 12 + y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $- 8 x - 4 y = - 12$ with $- 12 + y$ .

$- 8 (- 12 + y) - 4 y = - 12$

$x = - 12 + y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 8 (- 12 + y) - 4 y$ .

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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.

$- 8 \cdot - 12 - 8 y - 4 y = - 12$

$x = - 12 + y$

Step 2.2.1.1.2

Multiply $- 8$ by $- 12$ .

$96 - 8 y - 4 y = - 12$

$x = - 12 + y$

$96 - 8 y - 4 y = - 12$

$x = - 12 + y$

Step 2.2.1.2

Subtract $4 y$ from $- 8 y$ .

$96 - 12 y = - 12$

$x = - 12 + y$

$96 - 12 y = - 12$

$x = - 12 + y$

$96 - 12 y = - 12$

$x = - 12 + y$

$96 - 12 y = - 12$

$x = - 12 + y$

Step 3

Solve for $y$ in $96 - 12 y = - 12$ .

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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 $96$ from both sides of the equation.

$- 12 y = - 12 - 96$

$x = - 12 + y$

Step 3.1.2

Subtract $96$ from $- 12$ .

$- 12 y = - 108$

$x = - 12 + y$

$- 12 y = - 108$

$x = - 12 + y$

Step 3.2

Divide each term in $- 12 y = - 108$ by $- 12$ and simplify.

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Step 3.2.1

Divide each term in $- 12 y = - 108$ by $- 12$ .

$\frac{- 12 y}{- 12} = \frac{- 108}{- 12}$

$x = - 12 + y$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 12$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 12 y}{- 12} = \frac{- 108}{- 12}$

$x = - 12 + y$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 108}{- 12}$

$x = - 12 + y$

$y = \frac{- 108}{- 12}$

$x = - 12 + y$

$y = \frac{- 108}{- 12}$

$x = - 12 + y$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $- 108$ by $- 12$ .

$y = 9$

$x = - 12 + y$

$y = 9$

$x = - 12 + y$

$y = 9$

$x = - 12 + y$

$y = 9$

$x = - 12 + y$

Step 4

Replace all occurrences of $y$ with $9$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = - 12 + y$ with $9$ .

$x = - 12 + 9$

$y = 9$

Step 4.2

Simplify $x = - 12 + 9$ .

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Step 4.2.1

Simplify the left side.

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Step 4.2.1.1

Remove parentheses.

$x = - 12 + 9$

$y = 9$

$x = - 12 + 9$

$y = 9$

Step 4.2.2

Simplify the right side.

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Step 4.2.2.1

Add $- 12$ and $9$ .

$x = - 3$

$y = 9$

$x = - 3$

$y = 9$

$x = - 3$

$y = 9$

$x = - 3$

$y = 9$

Step 5

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

$(- 3, 9)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 3, 9)$

Equation Form:

$x = - 3, y = 9$

Step 7