Algebra Examples

$3 x - 4 y = - 8$ $8 y = 6 x - 16$

Step 1

Divide each term in $8 y = 6 x - 16$ by $8$ and simplify.

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Step 1.1

Divide each term in $8 y = 6 x - 16$ by $8$ .

$\frac{8 y}{8} = \frac{6 x}{8} + \frac{- 16}{8}$

$3 x - 4 y = - 8$

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.

$\frac{8 y}{8} = \frac{6 x}{8} + \frac{- 16}{8}$

$3 x - 4 y = - 8$

Step 1.2.1.2

Divide $y$ by $1$ .

$y = \frac{6 x}{8} + \frac{- 16}{8}$

$3 x - 4 y = - 8$

$y = \frac{6 x}{8} + \frac{- 16}{8}$

$3 x - 4 y = - 8$

$y = \frac{6 x}{8} + \frac{- 16}{8}$

$3 x - 4 y = - 8$

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 $6 x$ .

$y = \frac{2 (3 x)}{8} + \frac{- 16}{8}$

$3 x - 4 y = - 8$

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 $8$ .

$y = \frac{2 (3 x)}{2 (4)} + \frac{- 16}{8}$

$3 x - 4 y = - 8$

Step 1.3.1.1.2.2

Cancel the common factor.

$y = \frac{2 (3 x)}{2 \cdot 4} + \frac{- 16}{8}$

$3 x - 4 y = - 8$

Step 1.3.1.1.2.3

Rewrite the expression.

$y = \frac{3 x}{4} + \frac{- 16}{8}$

$3 x - 4 y = - 8$

$y = \frac{3 x}{4} + \frac{- 16}{8}$

$3 x - 4 y = - 8$

$y = \frac{3 x}{4} + \frac{- 16}{8}$

$3 x - 4 y = - 8$

Step 1.3.1.2

Divide $- 16$ by $8$ .

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

$3 x - 4 y = - 8$

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

$3 x - 4 y = - 8$

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

$3 x - 4 y = - 8$

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

$3 x - 4 y = - 8$

Step 2

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

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Step 2.1

Replace all occurrences of $y$ in $3 x - 4 y = - 8$ with $\frac{3 x}{4} - 2$ .

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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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.

$3 x - 4 \frac{3 x}{4} - 4 \cdot - 2 = - 8$

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

Step 2.2.1.1.2

Cancel the common factor of $4$ .

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Step 2.2.1.1.2.1

Factor $4$ out of $- 4$ .

$3 x + 4 (- 1) (\frac{3 x}{4}) - 4 \cdot - 2 = - 8$

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

Step 2.2.1.1.2.2

Cancel the common factor.

$3 x + 4 \cdot (- 1 \frac{3 x}{4}) - 4 \cdot - 2 = - 8$

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

Step 2.2.1.1.2.3

Rewrite the expression.

$3 x - 1 (3 x) - 4 \cdot - 2 = - 8$

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

$3 x - 1 (3 x) - 4 \cdot - 2 = - 8$

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

Step 2.2.1.1.3

Multiply $3$ by $- 1$ .

$3 x - 3 x - 4 \cdot - 2 = - 8$

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

Step 2.2.1.1.4

Multiply $- 4$ by $- 2$ .

$3 x - 3 x + 8 = - 8$

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

$3 x - 3 x + 8 = - 8$

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

Step 2.2.1.2

Simplify by adding terms.

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Step 2.2.1.2.1

Subtract $3 x$ from $3 x$ .

$0 + 8 = - 8$

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

Step 2.2.1.2.2

Add $0$ and $8$ .

$8 = - 8$

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

$8 = - 8$

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

$8 = - 8$

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

$8 = - 8$

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

$8 = - 8$

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

Step 3

Since $8 = - 8$ is not true, there is no solution.

No solution

Step 4