Precalculus Examples

$y = \frac{2}{3} x - 5$ , $(4, 7)$

Step 1

Insert the values of $x = 4$ and $y = 7$ into the equation to find if the ordered pair is a solution.

$7 = \frac{2}{3} \cdot (4) - 5$

Step 2

Simplify $\frac{2}{3} \cdot 4 - 5$ .

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Step 2.1

Multiply $\frac{2}{3} \cdot 4$ .

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Step 2.1.1

Combine $\frac{2}{3}$ and $4$ .

$7 = \frac{2 \cdot 4}{3} - 5$

Step 2.1.2

Multiply $2$ by $4$ .

$7 = \frac{8}{3} - 5$

Step 2.2

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$7 = \frac{8}{3} - 5 \cdot \frac{3}{3}$

Step 2.3

Combine $- 5$ and $\frac{3}{3}$ .

$7 = \frac{8}{3} + \frac{- 5 \cdot 3}{3}$

Step 2.4

Combine the numerators over the common denominator.

$7 = \frac{8 - 5 \cdot 3}{3}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 5$ by $3$ .

$7 = \frac{8 - 15}{3}$

Step 2.5.2

Subtract $15$ from $8$ .

$7 = \frac{- 7}{3}$

Step 2.6

Move the negative in front of the fraction.

$7 = - \frac{7}{3}$

Step 3

Since $7 \neq - \frac{7}{3}$ , there are no solutions.

No solution

Step 4

Since the equation is not true when the values are used, the ordered pair is not a solution.

The ordered pair is not a solution to the equation.