Finite Math Examples

(2, - 1)

$(2, - 1)$ ,

x^{2} + y^{2} - 6 x + 8 y = - 15

$x^{2} + y^{2} - 6 x + 8 y = - 15$

Step 1

Insert the values of

x = 2

$x = 2$ and

y = - 1

$y = - 1$ into the equation to find if the ordered pair is a solution.

{(2)}^{2} + {(- 1)}^{2} - 6 \cdot 2 + 8 (- 1) = - 15

${(2)}^{2} + {(- 1)}^{2} - 6 \cdot 2 + 8 (- 1) = - 15$

Step 2

Simplify

{(2)}^{2} + {(- 1)}^{2} - 6 \cdot 2 + 8 (- 1)

${(2)}^{2} + {(- 1)}^{2} - 6 \cdot 2 + 8 (- 1)$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Raise

2

$2$ to the power of

2

$2$ .

4 + {(- 1)}^{2} - 6 \cdot 2 + 8 (- 1) = - 15

$4 + {(- 1)}^{2} - 6 \cdot 2 + 8 (- 1) = - 15$

Step 2.1.2

Raise

- 1

$- 1$ to the power of

2

$2$ .

4 + 1 - 6 \cdot 2 + 8 (- 1) = - 15

$4 + 1 - 6 \cdot 2 + 8 (- 1) = - 15$

Step 2.1.3

Multiply

- 6

$- 6$ by

2

$2$ .

4 + 1 - 12 + 8 (- 1) = - 15

$4 + 1 - 12 + 8 (- 1) = - 15$

Step 2.1.4

Multiply

8

$8$ by

- 1

$- 1$ .

4 + 1 - 12 - 8 = - 15

$4 + 1 - 12 - 8 = - 15$

4 + 1 - 12 - 8 = - 15

$4 + 1 - 12 - 8 = - 15$

Step 2.2

Simplify by adding and subtracting.

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Step 2.2.1

Add

4

$4$ and

1

$1$ .

5 - 12 - 8 = - 15

$5 - 12 - 8 = - 15$

Step 2.2.2

Subtract

12

$12$ from

5

$5$ .

- 7 - 8 = - 15

$- 7 - 8 = - 15$

Step 2.2.3

Subtract

8

$8$ from

- 7

$- 7$ .

- 15 = - 15

$- 15 = - 15$

- 15 = - 15

$- 15 = - 15$

- 15 = - 15

$- 15 = - 15$

Step 3

Since

- 15 = - 15

$- 15 = - 15$ , 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.