Precalculus Examples

$y = - \frac{1}{3} x + 5$ , $(- 3, 2)$

Step 1

Insert the values of $x = - 3$ and $y = 2$ into the equation to find if the ordered pair is a solution.

$2 = - \frac{1}{3} \cdot - 3 + 5$

Step 2

Simplify $- \frac{1}{3} \cdot - 3 + 5$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Cancel the common factor of $3$ .

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Step 2.1.1.1

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$2 = \frac{- 1}{3} \cdot - 3 + 5$

Step 2.1.1.2

Factor $3$ out of $- 3$ .

$2 = \frac{- 1}{3} \cdot (3 (- 1)) + 5$

Step 2.1.1.3

Cancel the common factor.

$2 = \frac{- 1}{3} \cdot (3 \cdot - 1) + 5$

Step 2.1.1.4

Rewrite the expression.

$2 = - 1 \cdot - 1 + 5$

Step 2.1.2

Multiply $- 1$ by $- 1$ .

$2 = 1 + 5$

Step 2.2

Add $1$ and $5$ .

$2 = 6$

Step 3

Since $2 \neq 6$ , 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.