Algebra Examples

$y = 5 x - 7$ $- 3 x - 2 y = - 12$

Step 1

Add $3 x$ to both sides of the equation.

$- 2 y = - 12 + 3 x$

$y = 5 x - 7$

Step 2

Divide each term in $- 2 y = - 12 + 3 x$ by $- 2$ and simplify.

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Step 2.1

Divide each term in $- 2 y = - 12 + 3 x$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 12}{- 2} + \frac{3 x}{- 2}$

$y = 5 x - 7$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 12}{- 2} + \frac{3 x}{- 2}$

$y = 5 x - 7$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 12}{- 2} + \frac{3 x}{- 2}$

$y = 5 x - 7$

$y = \frac{- 12}{- 2} + \frac{3 x}{- 2}$

$y = 5 x - 7$

$y = \frac{- 12}{- 2} + \frac{3 x}{- 2}$

$y = 5 x - 7$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Divide $- 12$ by $- 2$ .

$y = 6 + \frac{3 x}{- 2}$

$y = 5 x - 7$

Step 2.3.1.2

Move the negative in front of the fraction.

$y = 6 - \frac{3 x}{2}$

$y = 5 x - 7$

$y = 6 - \frac{3 x}{2}$

$y = 5 x - 7$

$y = 6 - \frac{3 x}{2}$

$y = 5 x - 7$

$y = 6 - \frac{3 x}{2}$

$y = 5 x - 7$

Step 3

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

$(2, 3)$

Step 4