Algebra Examples

$- 7 x + 3 y = 1$ , $- 12 y = 28 x - 4$

Step 1

Add $7 x$ to both sides of the equation.

$3 y = 1 + 7 x$

$- 12 y = 28 x - 4$

Step 2

Divide each term in $3 y = 1 + 7 x$ by $3$ and simplify.

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Step 2.1

Divide each term in $3 y = 1 + 7 x$ by $3$ .

$\frac{3 y}{3} = \frac{1}{3} + \frac{7 x}{3}$

$- 12 y = 28 x - 4$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{1}{3} + \frac{7 x}{3}$

$- 12 y = 28 x - 4$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{1}{3} + \frac{7 x}{3}$

$- 12 y = 28 x - 4$

$y = \frac{1}{3} + \frac{7 x}{3}$

$- 12 y = 28 x - 4$

$y = \frac{1}{3} + \frac{7 x}{3}$

$- 12 y = 28 x - 4$

$y = \frac{1}{3} + \frac{7 x}{3}$

$- 12 y = 28 x - 4$

Step 3

Divide each term in $- 12 y = 28 x - 4$ by $- 12$ and simplify.

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Step 3.1

Divide each term in $- 12 y = 28 x - 4$ by $- 12$ .

$\frac{- 12 y}{- 12} = \frac{28 x}{- 12} + \frac{- 4}{- 12}$

$y = \frac{1}{3} + \frac{7 x}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 12$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 12 y}{- 12} = \frac{28 x}{- 12} + \frac{- 4}{- 12}$

$y = \frac{1}{3} + \frac{7 x}{3}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{28 x}{- 12} + \frac{- 4}{- 12}$

$y = \frac{1}{3} + \frac{7 x}{3}$

$y = \frac{28 x}{- 12} + \frac{- 4}{- 12}$

$y = \frac{1}{3} + \frac{7 x}{3}$

$y = \frac{28 x}{- 12} + \frac{- 4}{- 12}$

$y = \frac{1}{3} + \frac{7 x}{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Cancel the common factor of $28$ and $- 12$ .

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Step 3.3.1.1.1

Factor $4$ out of $28 x$ .

$y = \frac{4 (7 x)}{- 12} + \frac{- 4}{- 12}$

$y = \frac{1}{3} + \frac{7 x}{3}$

Step 3.3.1.1.2

Cancel the common factors.

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Step 3.3.1.1.2.1

Factor $4$ out of $- 12$ .

$y = \frac{4 (7 x)}{4 (- 3)} + \frac{- 4}{- 12}$

$y = \frac{1}{3} + \frac{7 x}{3}$

Step 3.3.1.1.2.2

Cancel the common factor.

$y = \frac{4 (7 x)}{4 \cdot - 3} + \frac{- 4}{- 12}$

$y = \frac{1}{3} + \frac{7 x}{3}$

Step 3.3.1.1.2.3

Rewrite the expression.

$y = \frac{7 x}{- 3} + \frac{- 4}{- 12}$

$y = \frac{1}{3} + \frac{7 x}{3}$

$y = \frac{7 x}{- 3} + \frac{- 4}{- 12}$

$y = \frac{1}{3} + \frac{7 x}{3}$

$y = \frac{7 x}{- 3} + \frac{- 4}{- 12}$

$y = \frac{1}{3} + \frac{7 x}{3}$

Step 3.3.1.2

Move the negative in front of the fraction.

$y = - \frac{7 x}{3} + \frac{- 4}{- 12}$

$y = \frac{1}{3} + \frac{7 x}{3}$

Step 3.3.1.3

Cancel the common factor of $- 4$ and $- 12$ .

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Step 3.3.1.3.1

Factor $- 4$ out of $- 4$ .

$y = - \frac{7 x}{3} + \frac{- 4 \cdot 1}{- 12}$

$y = \frac{1}{3} + \frac{7 x}{3}$

Step 3.3.1.3.2

Cancel the common factors.

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Step 3.3.1.3.2.1

Factor $- 4$ out of $- 12$ .

$y = - \frac{7 x}{3} + \frac{- 4 \cdot 1}{- 4 \cdot 3}$

$y = \frac{1}{3} + \frac{7 x}{3}$

Step 3.3.1.3.2.2

Cancel the common factor.

$y = - \frac{7 x}{3} + \frac{- 4 \cdot 1}{- 4 \cdot 3}$

$y = \frac{1}{3} + \frac{7 x}{3}$

Step 3.3.1.3.2.3

Rewrite the expression.

$y = - \frac{7 x}{3} + \frac{1}{3}$

$y = \frac{1}{3} + \frac{7 x}{3}$

$y = - \frac{7 x}{3} + \frac{1}{3}$

$y = \frac{1}{3} + \frac{7 x}{3}$

$y = - \frac{7 x}{3} + \frac{1}{3}$

$y = \frac{1}{3} + \frac{7 x}{3}$

$y = - \frac{7 x}{3} + \frac{1}{3}$

$y = \frac{1}{3} + \frac{7 x}{3}$

$y = - \frac{7 x}{3} + \frac{1}{3}$

$y = \frac{1}{3} + \frac{7 x}{3}$

$y = - \frac{7 x}{3} + \frac{1}{3}$

$y = \frac{1}{3} + \frac{7 x}{3}$

Step 4

Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution.

$(0, \frac{1}{3})$

Step 5