Finite Math Examples

$y = - 2 x^{2} + 3 x - 2$ , $(2, - 3)$

Step 1

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

$- 3 = - 2 {(2)}^{2} + 3 (2) - 2$

Step 2

Simplify $- 2 \cdot 2^{2} + 3 (2) - 2$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

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

$- 3 = - 2 \cdot 4 + 3 (2) - 2$

Step 2.1.2

Multiply $- 2$ by $4$ .

$- 3 = - 8 + 3 (2) - 2$

Step 2.1.3

Multiply $3$ by $2$ .

$- 3 = - 8 + 6 - 2$

Step 2.2

Simplify by adding and subtracting.

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Step 2.2.1

Add $- 8$ and $6$ .

$- 3 = - 2 - 2$

Step 2.2.2

Subtract $2$ from $- 2$ .

$- 3 = - 4$

Step 3

Since $- 3 \neq - 4$ , 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.