Precalculus Examples

$7 x - 3 y = 5$ , $(- \frac{1}{7}, - 2)$

Step 1

Insert the values of $x = - \frac{1}{7}$ and $y = - 2$ into the equation to find if the ordered pair is a solution.

$7 (- \frac{1}{7}) - 3 \cdot - 2 = 5$

Step 2

Simplify $7 (- \frac{1}{7}) - 3 \cdot - 2$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Cancel the common factor of $7$ .

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Step 2.1.1.1

Move the leading negative in $- \frac{1}{7}$ into the numerator.

$7 (\frac{- 1}{7}) - 3 \cdot - 2 = 5$

Step 2.1.1.2

Cancel the common factor.

$7 (\frac{- 1}{7}) - 3 \cdot - 2 = 5$

Step 2.1.1.3

Rewrite the expression.

$- 1 - 3 \cdot - 2 = 5$

Step 2.1.2

Multiply $- 3$ by $- 2$ .

$- 1 + 6 = 5$

Step 2.2

Add $- 1$ and $6$ .

$5 = 5$

Step 3

Since $5 = 5$ , the equation will always be true.

Always true

Step 4

Since the equation is always true when the values are used, the ordered pair is a solution.

The ordered pair is a solution to the equation.