Precalculus Examples

$\frac{- 7}{2} x - y = - 18$ , $8 x^{2} - 2 y^{3} = 0$

Step 1

Simplify each term.

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Step 1.1

Move the negative in front of the fraction.

$- \frac{7}{2} x - y = - 18$

$8 x^{2} - 2 y^{3} = 0$

Step 1.2

Combine $x$ and $\frac{7}{2}$ .

$- \frac{x \cdot 7}{2} - y = - 18$

$8 x^{2} - 2 y^{3} = 0$

Step 1.3

Move $7$ to the left of $x$ .

$- \frac{7 x}{2} - y = - 18$

$8 x^{2} - 2 y^{3} = 0$

$- \frac{7 x}{2} - y = - 18$

$8 x^{2} - 2 y^{3} = 0$

Step 2

Add $\frac{7 x}{2}$ to both sides of the equation.

$- y = - 18 + \frac{7 x}{2}$

$8 x^{2} - 2 y^{3} = 0$

Step 3

Divide each term in $- y = - 18 + \frac{7 x}{2}$ by $- 1$ and simplify.

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Step 3.1

Divide each term in $- y = - 18 + \frac{7 x}{2}$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 18}{- 1} + \frac{\frac{7 x}{2}}{- 1}$

$8 x^{2} - 2 y^{3} = 0$

Step 3.2

Simplify the left side.

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Step 3.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 18}{- 1} + \frac{\frac{7 x}{2}}{- 1}$

$8 x^{2} - 2 y^{3} = 0$

Step 3.2.2

Divide $y$ by $1$ .

$y = \frac{- 18}{- 1} + \frac{\frac{7 x}{2}}{- 1}$

$8 x^{2} - 2 y^{3} = 0$

$y = \frac{- 18}{- 1} + \frac{\frac{7 x}{2}}{- 1}$

$8 x^{2} - 2 y^{3} = 0$

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

Divide $- 18$ by $- 1$ .

$y = 18 + \frac{\frac{7 x}{2}}{- 1}$

$8 x^{2} - 2 y^{3} = 0$

Step 3.3.1.2

Move the negative one from the denominator of $\frac{\frac{7 x}{2}}{- 1}$ .

$y = 18 - 1 \cdot \frac{7 x}{2}$

$8 x^{2} - 2 y^{3} = 0$

Step 3.3.1.3

Rewrite $- 1 \cdot \frac{7 x}{2}$ as $- \frac{7 x}{2}$ .

$y = 18 - \frac{7 x}{2}$

$8 x^{2} - 2 y^{3} = 0$

$y = 18 - \frac{7 x}{2}$

$8 x^{2} - 2 y^{3} = 0$

$y = 18 - \frac{7 x}{2}$

$8 x^{2} - 2 y^{3} = 0$

$y = 18 - \frac{7 x}{2}$

$8 x^{2} - 2 y^{3} = 0$

Step 4

Subtract $8 x^{2}$ from both sides of the equation.

$- 2 y^{3} = - 8 x^{2}$

$y = 18 - \frac{7 x}{2}$

Step 5

Divide each term in $- 2 y^{3} = - 8 x^{2}$ by $- 2$ and simplify.

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Step 5.1

Divide each term in $- 2 y^{3} = - 8 x^{2}$ by $- 2$ .

$\frac{- 2 y^{3}}{- 2} = \frac{- 8 x^{2}}{- 2}$

$y = 18 - \frac{7 x}{2}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $- 2$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{- 2 y^{3}}{- 2} = \frac{- 8 x^{2}}{- 2}$

$y = 18 - \frac{7 x}{2}$

Step 5.2.1.2

Divide $y^{3}$ by $1$ .

$y^{3} = \frac{- 8 x^{2}}{- 2}$

$y = 18 - \frac{7 x}{2}$

$y^{3} = \frac{- 8 x^{2}}{- 2}$

$y = 18 - \frac{7 x}{2}$

$y^{3} = \frac{- 8 x^{2}}{- 2}$

$y = 18 - \frac{7 x}{2}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Cancel the common factor of $- 8$ and $- 2$ .

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Step 5.3.1.1

Factor $- 2$ out of $- 8 x^{2}$ .

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

$y = 18 - \frac{7 x}{2}$

Step 5.3.1.2

Cancel the common factors.

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Step 5.3.1.2.1

Factor $- 2$ out of $- 2$ .

$y^{3} = \frac{- 2 (4 x^{2})}{- 2 \cdot 1}$

$y = 18 - \frac{7 x}{2}$

Step 5.3.1.2.2

Cancel the common factor.

$y^{3} = \frac{- 2 (4 x^{2})}{- 2 \cdot 1}$

$y = 18 - \frac{7 x}{2}$

Step 5.3.1.2.3

Rewrite the expression.

$y^{3} = \frac{4 x^{2}}{1}$

$y = 18 - \frac{7 x}{2}$

Step 5.3.1.2.4

Divide $4 x^{2}$ by $1$ .

$y^{3} = 4 x^{2}$

$y = 18 - \frac{7 x}{2}$

$y^{3} = 4 x^{2}$

$y = 18 - \frac{7 x}{2}$

$y^{3} = 4 x^{2}$

$y = 18 - \frac{7 x}{2}$

$y^{3} = 4 x^{2}$

$y = 18 - \frac{7 x}{2}$

$y^{3} = 4 x^{2}$

$y = 18 - \frac{7 x}{2}$

Step 6

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$y = \sqrt[3]{4 x^{2}}$

$y = 18 - \frac{7 x}{2}$

Step 7

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

$(4, 4)$

Step 8