Precalculus Examples

${(x - 8)}^{2} + {(y + 6)}^{2} = - 9$ , $(4, - 1)$

Step 1

Insert the values of $x = 4$ and $y = - 1$ into the equation to find if the ordered pair is a solution.

${((4) - 8)}^{2} + {((- 1) + 6)}^{2} = - 9$

Step 2

Simplify ${((4) - 8)}^{2} + {((- 1) + 6)}^{2}$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Subtract $8$ from $4$ .

${(- 4)}^{2} + {((- 1) + 6)}^{2} = - 9$

Step 2.1.2

Raise $- 4$ to the power of $2$ .

$16 + {((- 1) + 6)}^{2} = - 9$

Step 2.1.3

Add $- 1$ and $6$ .

$16 + 5^{2} = - 9$

Step 2.1.4

Raise $5$ to the power of $2$ .

$16 + 25 = - 9$

Step 2.2

Add $16$ and $25$ .

$41 = - 9$

Step 3

Since $41 \neq - 9$ , 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.