Algebra Examples

$x - y = 12$ and $x + 7 y = - 20$

Step 1

Add $y$ to both sides of the equation.

$x = 12 + y$

$x + 7 y = - 20$

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 $x + 7 y = - 20$ with $12 + y$ .

$(12 + y) + 7 y = - 20$

$x = 12 + y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Add $y$ and $7 y$ .

$12 + 8 y = - 20$

$x = 12 + y$

$12 + 8 y = - 20$

$x = 12 + y$

$12 + 8 y = - 20$

$x = 12 + y$

Step 3

Solve for $y$ in $12 + 8 y = - 20$ .

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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.

$8 y = - 20 - 12$

$x = 12 + y$

Step 3.1.2

Subtract $12$ from $- 20$ .

$8 y = - 32$

$x = 12 + y$

$8 y = - 32$

$x = 12 + y$

Step 3.2

Divide each term in $8 y = - 32$ by $8$ and simplify.

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Step 3.2.1

Divide each term in $8 y = - 32$ by $8$ .

$\frac{8 y}{8} = \frac{- 32}{8}$

$x = 12 + y$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $8$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{8 y}{8} = \frac{- 32}{8}$

$x = 12 + y$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 32}{8}$

$x = 12 + y$

$y = \frac{- 32}{8}$

$x = 12 + y$

$y = \frac{- 32}{8}$

$x = 12 + y$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $- 32$ by $8$ .

$y = - 4$

$x = 12 + y$

$y = - 4$

$x = 12 + y$

$y = - 4$

$x = 12 + y$

$y = - 4$

$x = 12 + y$

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 $x = 12 + y$ with $- 4$ .

$x = 12 - 4$

$y = - 4$

Step 4.2

Simplify $x = 12 - 4$ .

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Step 4.2.1

Simplify the left side.

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Step 4.2.1.1

Remove parentheses.

$x = 12 - 4$

$y = - 4$

$x = 12 - 4$

$y = - 4$

Step 4.2.2

Simplify the right side.

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Step 4.2.2.1

Subtract $4$ from $12$ .

$x = 8$

$y = - 4$

$x = 8$

$y = - 4$

$x = 8$

$y = - 4$

$x = 8$

$y = - 4$

Step 5

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

$(8, - 4)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(8, - 4)$

Equation Form:

$x = 8, y = - 4$

Step 7