Finite Math Examples

$(2, - 1)$ , $x^{2} + y^{2} - 6 x + 8 y = - 15$

Step 1

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

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

Step 2

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

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

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

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

Step 2.1.2

Raise $- 1$ to the power of $2$ .

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

Step 2.1.3

Multiply $- 6$ by $2$ .

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

Step 2.1.4

Multiply $8$ by $- 1$ .

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

Step 2.2

Simplify by adding and subtracting.

Tap for more steps...

Step 2.2.1

Add $4$ and $1$ .

$5 - 12 - 8 = - 15$

Step 2.2.2

Subtract $12$ from $5$ .

$- 7 - 8 = - 15$

Step 2.2.3

Subtract $8$ from $- 7$ .

$- 15 = - 15$

Step 3

Since $- 15 = - 15$ , 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.