Algebra Examples

$9 x + 15 y = 6$ $5 y = - 3 x + 4$

Step 1

Divide each term in $5 y = - 3 x + 4$ by $5$ and simplify.

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Step 1.1

Divide each term in $5 y = - 3 x + 4$ by $5$ .

$\frac{5 y}{5} = \frac{- 3 x}{5} + \frac{4}{5}$

$9 x + 15 y = 6$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $5$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{- 3 x}{5} + \frac{4}{5}$

$9 x + 15 y = 6$

Step 1.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 3 x}{5} + \frac{4}{5}$

$9 x + 15 y = 6$

$y = \frac{- 3 x}{5} + \frac{4}{5}$

$9 x + 15 y = 6$

$y = \frac{- 3 x}{5} + \frac{4}{5}$

$9 x + 15 y = 6$

Step 1.3

Simplify the right side.

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Step 1.3.1

Move the negative in front of the fraction.

$y = - \frac{3 x}{5} + \frac{4}{5}$

$9 x + 15 y = 6$

$y = - \frac{3 x}{5} + \frac{4}{5}$

$9 x + 15 y = 6$

$y = - \frac{3 x}{5} + \frac{4}{5}$

$9 x + 15 y = 6$

Step 2

Replace all occurrences of $y$ with $- \frac{3 x}{5} + \frac{4}{5}$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $9 x + 15 y = 6$ with $- \frac{3 x}{5} + \frac{4}{5}$ .

$9 x + 15 (- \frac{3 x}{5} + \frac{4}{5}) = 6$

$y = - \frac{3 x}{5} + \frac{4}{5}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $9 x + 15 (- \frac{3 x}{5} + \frac{4}{5})$ .

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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.

$9 x + 15 (- \frac{3 x}{5}) + 15 (\frac{4}{5}) = 6$

$y = - \frac{3 x}{5} + \frac{4}{5}$

Step 2.2.1.1.2

Cancel the common factor of $5$ .

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Step 2.2.1.1.2.1

Move the leading negative in $- \frac{3 x}{5}$ into the numerator.

$9 x + 15 (\frac{- 3 x}{5}) + 15 (\frac{4}{5}) = 6$

$y = - \frac{3 x}{5} + \frac{4}{5}$

Step 2.2.1.1.2.2

Factor $5$ out of $15$ .

$9 x + 5 (3) (\frac{- 3 x}{5}) + 15 (\frac{4}{5}) = 6$

$y = - \frac{3 x}{5} + \frac{4}{5}$

Step 2.2.1.1.2.3

Cancel the common factor.

$9 x + 5 \cdot (3 (\frac{- 3 x}{5})) + 15 (\frac{4}{5}) = 6$

$y = - \frac{3 x}{5} + \frac{4}{5}$

Step 2.2.1.1.2.4

Rewrite the expression.

$9 x + 3 (- 3 x) + 15 (\frac{4}{5}) = 6$

$y = - \frac{3 x}{5} + \frac{4}{5}$

$9 x + 3 (- 3 x) + 15 (\frac{4}{5}) = 6$

$y = - \frac{3 x}{5} + \frac{4}{5}$

Step 2.2.1.1.3

Multiply $- 3$ by $3$ .

$9 x - 9 x + 15 (\frac{4}{5}) = 6$

$y = - \frac{3 x}{5} + \frac{4}{5}$

Step 2.2.1.1.4

Cancel the common factor of $5$ .

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Step 2.2.1.1.4.1

Factor $5$ out of $15$ .

$9 x - 9 x + 5 (3) (\frac{4}{5}) = 6$

$y = - \frac{3 x}{5} + \frac{4}{5}$

Step 2.2.1.1.4.2

Cancel the common factor.

$9 x - 9 x + 5 \cdot (3 (\frac{4}{5})) = 6$

$y = - \frac{3 x}{5} + \frac{4}{5}$

Step 2.2.1.1.4.3

Rewrite the expression.

$9 x - 9 x + 3 \cdot 4 = 6$

$y = - \frac{3 x}{5} + \frac{4}{5}$

$9 x - 9 x + 3 \cdot 4 = 6$

$y = - \frac{3 x}{5} + \frac{4}{5}$

Step 2.2.1.1.5

Multiply $3$ by $4$ .

$9 x - 9 x + 12 = 6$

$y = - \frac{3 x}{5} + \frac{4}{5}$

$9 x - 9 x + 12 = 6$

$y = - \frac{3 x}{5} + \frac{4}{5}$

Step 2.2.1.2

Simplify by adding terms.

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Step 2.2.1.2.1

Subtract $9 x$ from $9 x$ .

$0 + 12 = 6$

$y = - \frac{3 x}{5} + \frac{4}{5}$

Step 2.2.1.2.2

Add $0$ and $12$ .

$12 = 6$

$y = - \frac{3 x}{5} + \frac{4}{5}$

$12 = 6$

$y = - \frac{3 x}{5} + \frac{4}{5}$

$12 = 6$

$y = - \frac{3 x}{5} + \frac{4}{5}$

$12 = 6$

$y = - \frac{3 x}{5} + \frac{4}{5}$

$12 = 6$

$y = - \frac{3 x}{5} + \frac{4}{5}$

Step 3

Since $12 = 6$ is not true, there is no solution.

No solution

Step 4