Precalculus Examples

$3 x + 5 y = - 23$ , $4 x + 2 y = - 12$

Step 1

Subtract $3 x$ from both sides of the equation.

$5 y = - 23 - 3 x$

$4 x + 2 y = - 12$

Step 2

Divide each term in $5 y = - 23 - 3 x$ by $5$ and simplify.

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Step 2.1

Divide each term in $5 y = - 23 - 3 x$ by $5$ .

$\frac{5 y}{5} = \frac{- 23}{5} + \frac{- 3 x}{5}$

$4 x + 2 y = - 12$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $5$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{- 23}{5} + \frac{- 3 x}{5}$

$4 x + 2 y = - 12$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 23}{5} + \frac{- 3 x}{5}$

$4 x + 2 y = - 12$

$y = \frac{- 23}{5} + \frac{- 3 x}{5}$

$4 x + 2 y = - 12$

$y = \frac{- 23}{5} + \frac{- 3 x}{5}$

$4 x + 2 y = - 12$

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

Move the negative in front of the fraction.

$y = - \frac{23}{5} + \frac{- 3 x}{5}$

$4 x + 2 y = - 12$

Step 2.3.1.2

Move the negative in front of the fraction.

$y = - \frac{23}{5} - \frac{3 x}{5}$

$4 x + 2 y = - 12$

$y = - \frac{23}{5} - \frac{3 x}{5}$

$4 x + 2 y = - 12$

$y = - \frac{23}{5} - \frac{3 x}{5}$

$4 x + 2 y = - 12$

$y = - \frac{23}{5} - \frac{3 x}{5}$

$4 x + 2 y = - 12$

Step 3

Subtract $4 x$ from both sides of the equation.

$2 y = - 12 - 4 x$

$y = - \frac{23}{5} - \frac{3 x}{5}$

Step 4

Divide each term in $2 y = - 12 - 4 x$ by $2$ and simplify.

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Step 4.1

Divide each term in $2 y = - 12 - 4 x$ by $2$ .

$\frac{2 y}{2} = \frac{- 12}{2} + \frac{- 4 x}{2}$

$y = - \frac{23}{5} - \frac{3 x}{5}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{- 12}{2} + \frac{- 4 x}{2}$

$y = - \frac{23}{5} - \frac{3 x}{5}$

Step 4.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 12}{2} + \frac{- 4 x}{2}$

$y = - \frac{23}{5} - \frac{3 x}{5}$

$y = \frac{- 12}{2} + \frac{- 4 x}{2}$

$y = - \frac{23}{5} - \frac{3 x}{5}$

$y = \frac{- 12}{2} + \frac{- 4 x}{2}$

$y = - \frac{23}{5} - \frac{3 x}{5}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Divide $- 12$ by $2$ .

$y = - 6 + \frac{- 4 x}{2}$

$y = - \frac{23}{5} - \frac{3 x}{5}$

Step 4.3.1.2

Cancel the common factor of $- 4$ and $2$ .

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Step 4.3.1.2.1

Factor $2$ out of $- 4 x$ .

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

$y = - \frac{23}{5} - \frac{3 x}{5}$

Step 4.3.1.2.2

Cancel the common factors.

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Step 4.3.1.2.2.1

Factor $2$ out of $2$ .

$y = - 6 + \frac{2 (- 2 x)}{2 (1)}$

$y = - \frac{23}{5} - \frac{3 x}{5}$

Step 4.3.1.2.2.2

Cancel the common factor.

$y = - 6 + \frac{2 (- 2 x)}{2 \cdot 1}$

$y = - \frac{23}{5} - \frac{3 x}{5}$

Step 4.3.1.2.2.3

Rewrite the expression.

$y = - 6 + \frac{- 2 x}{1}$

$y = - \frac{23}{5} - \frac{3 x}{5}$

Step 4.3.1.2.2.4

Divide $- 2 x$ by $1$ .

$y = - 6 - 2 x$

$y = - \frac{23}{5} - \frac{3 x}{5}$

$y = - 6 - 2 x$

$y = - \frac{23}{5} - \frac{3 x}{5}$

$y = - 6 - 2 x$

$y = - \frac{23}{5} - \frac{3 x}{5}$

$y = - 6 - 2 x$

$y = - \frac{23}{5} - \frac{3 x}{5}$

$y = - 6 - 2 x$

$y = - \frac{23}{5} - \frac{3 x}{5}$

$y = - 6 - 2 x$

$y = - \frac{23}{5} - \frac{3 x}{5}$

Step 5

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

$(- 1, - 4)$

Step 6