Algebra Examples

$- 3 x - 4 y = 2$ , $8 y = - 6 x - 4$

Step 1

Divide each term in $8 y = - 6 x - 4$ by $8$ and simplify.

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Step 1.1

Divide each term in $8 y = - 6 x - 4$ by $8$ .

$\frac{8 y}{8} = \frac{- 6 x}{8} + \frac{- 4}{8}$

$- 3 x - 4 y = 2$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $8$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{8 y}{8} = \frac{- 6 x}{8} + \frac{- 4}{8}$

$- 3 x - 4 y = 2$

Step 1.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 6 x}{8} + \frac{- 4}{8}$

$- 3 x - 4 y = 2$

$y = \frac{- 6 x}{8} + \frac{- 4}{8}$

$- 3 x - 4 y = 2$

$y = \frac{- 6 x}{8} + \frac{- 4}{8}$

$- 3 x - 4 y = 2$

Step 1.3

Simplify the right side.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Cancel the common factor of $- 6$ and $8$ .

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Step 1.3.1.1.1

Factor $2$ out of $- 6 x$ .

$y = \frac{2 (- 3 x)}{8} + \frac{- 4}{8}$

$- 3 x - 4 y = 2$

Step 1.3.1.1.2

Cancel the common factors.

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Step 1.3.1.1.2.1

Factor $2$ out of $8$ .

$y = \frac{2 (- 3 x)}{2 (4)} + \frac{- 4}{8}$

$- 3 x - 4 y = 2$

Step 1.3.1.1.2.2

Cancel the common factor.

$y = \frac{2 (- 3 x)}{2 \cdot 4} + \frac{- 4}{8}$

$- 3 x - 4 y = 2$

Step 1.3.1.1.2.3

Rewrite the expression.

$y = \frac{- 3 x}{4} + \frac{- 4}{8}$

$- 3 x - 4 y = 2$

$y = \frac{- 3 x}{4} + \frac{- 4}{8}$

$- 3 x - 4 y = 2$

$y = \frac{- 3 x}{4} + \frac{- 4}{8}$

$- 3 x - 4 y = 2$

Step 1.3.1.2

Move the negative in front of the fraction.

$y = - \frac{3 x}{4} + \frac{- 4}{8}$

$- 3 x - 4 y = 2$

Step 1.3.1.3

Cancel the common factor of $- 4$ and $8$ .

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Step 1.3.1.3.1

Factor $4$ out of $- 4$ .

$y = - \frac{3 x}{4} + \frac{4 (- 1)}{8}$

$- 3 x - 4 y = 2$

Step 1.3.1.3.2

Cancel the common factors.

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Step 1.3.1.3.2.1

Factor $4$ out of $8$ .

$y = - \frac{3 x}{4} + \frac{4 \cdot - 1}{4 \cdot 2}$

$- 3 x - 4 y = 2$

Step 1.3.1.3.2.2

Cancel the common factor.

$y = - \frac{3 x}{4} + \frac{4 \cdot - 1}{4 \cdot 2}$

$- 3 x - 4 y = 2$

Step 1.3.1.3.2.3

Rewrite the expression.

$y = - \frac{3 x}{4} + \frac{- 1}{2}$

$- 3 x - 4 y = 2$

$y = - \frac{3 x}{4} + \frac{- 1}{2}$

$- 3 x - 4 y = 2$

$y = - \frac{3 x}{4} + \frac{- 1}{2}$

$- 3 x - 4 y = 2$

Step 1.3.1.4

Move the negative in front of the fraction.

$y = - \frac{3 x}{4} - \frac{1}{2}$

$- 3 x - 4 y = 2$

$y = - \frac{3 x}{4} - \frac{1}{2}$

$- 3 x - 4 y = 2$

$y = - \frac{3 x}{4} - \frac{1}{2}$

$- 3 x - 4 y = 2$

$y = - \frac{3 x}{4} - \frac{1}{2}$

$- 3 x - 4 y = 2$

Step 2

Replace all occurrences of $y$ with $- \frac{3 x}{4} - \frac{1}{2}$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $- 3 x - 4 y = 2$ with $- \frac{3 x}{4} - \frac{1}{2}$ .

$- 3 x - 4 (- \frac{3 x}{4} - \frac{1}{2}) = 2$

$y = - \frac{3 x}{4} - \frac{1}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 3 x - 4 (- \frac{3 x}{4} - \frac{1}{2})$ .

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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.

$- 3 x - 4 (- \frac{3 x}{4}) - 4 (- \frac{1}{2}) = 2$

$y = - \frac{3 x}{4} - \frac{1}{2}$

Step 2.2.1.1.2

Cancel the common factor of $4$ .

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Step 2.2.1.1.2.1

Move the leading negative in $- \frac{3 x}{4}$ into the numerator.

$- 3 x - 4 \frac{- 3 x}{4} - 4 (- \frac{1}{2}) = 2$

$y = - \frac{3 x}{4} - \frac{1}{2}$

Step 2.2.1.1.2.2

Factor $4$ out of $- 4$ .

$- 3 x + 4 (- 1) (\frac{- 3 x}{4}) - 4 (- \frac{1}{2}) = 2$

$y = - \frac{3 x}{4} - \frac{1}{2}$

Step 2.2.1.1.2.3

Cancel the common factor.

$- 3 x + 4 \cdot (- 1 \frac{- 3 x}{4}) - 4 (- \frac{1}{2}) = 2$

$y = - \frac{3 x}{4} - \frac{1}{2}$

Step 2.2.1.1.2.4

Rewrite the expression.

$- 3 x - 1 (- 3 x) - 4 (- \frac{1}{2}) = 2$

$y = - \frac{3 x}{4} - \frac{1}{2}$

$- 3 x - 1 (- 3 x) - 4 (- \frac{1}{2}) = 2$

$y = - \frac{3 x}{4} - \frac{1}{2}$

Step 2.2.1.1.3

Multiply $- 3$ by $- 1$ .

$- 3 x + 3 x - 4 (- \frac{1}{2}) = 2$

$y = - \frac{3 x}{4} - \frac{1}{2}$

Step 2.2.1.1.4

Cancel the common factor of $2$ .

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Step 2.2.1.1.4.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$- 3 x + 3 x - 4 (\frac{- 1}{2}) = 2$

$y = - \frac{3 x}{4} - \frac{1}{2}$

Step 2.2.1.1.4.2

Factor $2$ out of $- 4$ .

$- 3 x + 3 x + 2 (- 2) (\frac{- 1}{2}) = 2$

$y = - \frac{3 x}{4} - \frac{1}{2}$

Step 2.2.1.1.4.3

Cancel the common factor.

$- 3 x + 3 x + 2 \cdot (- 2 (\frac{- 1}{2})) = 2$

$y = - \frac{3 x}{4} - \frac{1}{2}$

Step 2.2.1.1.4.4

Rewrite the expression.

$- 3 x + 3 x - 2 \cdot - 1 = 2$

$y = - \frac{3 x}{4} - \frac{1}{2}$

$- 3 x + 3 x - 2 \cdot - 1 = 2$

$y = - \frac{3 x}{4} - \frac{1}{2}$

Step 2.2.1.1.5

Multiply $- 2$ by $- 1$ .

$- 3 x + 3 x + 2 = 2$

$y = - \frac{3 x}{4} - \frac{1}{2}$

$- 3 x + 3 x + 2 = 2$

$y = - \frac{3 x}{4} - \frac{1}{2}$

Step 2.2.1.2

Simplify by adding terms.

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Step 2.2.1.2.1

Add $- 3 x$ and $3 x$ .

$0 + 2 = 2$

$y = - \frac{3 x}{4} - \frac{1}{2}$

Step 2.2.1.2.2

Add $0$ and $2$ .

$2 = 2$

$y = - \frac{3 x}{4} - \frac{1}{2}$

$2 = 2$

$y = - \frac{3 x}{4} - \frac{1}{2}$

$2 = 2$

$y = - \frac{3 x}{4} - \frac{1}{2}$

$2 = 2$

$y = - \frac{3 x}{4} - \frac{1}{2}$

$2 = 2$

$y = - \frac{3 x}{4} - \frac{1}{2}$

Step 3

Remove any equations from the system that are always true.

$y = - \frac{3 x}{4} - \frac{1}{2}$

Step 4