Calculus Examples

$2 {(x)}^{2} + y^{2} = 41$ , $(4, 3)$

Step 1

Insert the values of $x = 4$ and $y = 3$ into the equation to find if the ordered pair is a solution.

$2 {(4)}^{2} + {(3)}^{2} = 41$

Step 2

Simplify $2 {(4)}^{2} + {(3)}^{2}$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

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

$2 \cdot 16 + {(3)}^{2} = 41$

Step 2.1.2

Multiply $2$ by $16$ .

$32 + {(3)}^{2} = 41$

Step 2.1.3

Raise $3$ to the power of $2$ .

$32 + 9 = 41$

Step 2.2

Add $32$ and $9$ .

$41 = 41$

Step 3

Since $41 = 41$ , 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.