Algebra Examples

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

Step 1

Rewrite the equation as $16 - 4 y = x$ .

$16 - 4 y = x$

$3 x + 4 y = 8$

Step 2

Subtract $16$ from both sides of the equation.

$- 4 y = x - 16$

$3 x + 4 y = 8$

Step 3

Divide each term in $- 4 y = x - 16$ by $- 4$ and simplify.

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Step 3.1

Divide each term in $- 4 y = x - 16$ by $- 4$ .

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

$3 x + 4 y = 8$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 4$ .

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Step 3.2.1.1

Cancel the common factor.

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

$3 x + 4 y = 8$

Step 3.2.1.2

Divide $y$ by $1$ .

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

$3 x + 4 y = 8$

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

$3 x + 4 y = 8$

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

$3 x + 4 y = 8$

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

Move the negative in front of the fraction.

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

$3 x + 4 y = 8$

Step 3.3.1.2

Divide $- 16$ by $- 4$ .

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

$3 x + 4 y = 8$

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

$3 x + 4 y = 8$

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

$3 x + 4 y = 8$

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

$3 x + 4 y = 8$

Step 4

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

$4 y = 8 - 3 x$

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

Step 5

Divide each term in $4 y = 8 - 3 x$ by $4$ and simplify.

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Step 5.1

Divide each term in $4 y = 8 - 3 x$ by $4$ .

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

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

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $4$ .

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Step 5.2.1.1

Cancel the common factor.

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

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

Step 5.2.1.2

Divide $y$ by $1$ .

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

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

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

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

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

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

Step 5.3

Simplify the right side.

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Step 5.3.1

Simplify each term.

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Step 5.3.1.1

Divide $8$ by $4$ .

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

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

Step 5.3.1.2

Move the negative in front of the fraction.

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

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

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

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

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

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

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

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

Step 6

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

$(- 4, 5)$

Step 7