Determine if (0,0) is a Solution

$x^{3} + 2 y^{2} + x < 2$ , $(0, 0)$

Step 1

Insert the values of $x = 0$ and $y = 0$ into the equation to find if the ordered pair is a solution.

${(0)}^{3} + 2 {(0)}^{2} + 0 < 2$

Step 2

Simplify ${(0)}^{3} + 2 {(0)}^{2} + 0$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Raising $0$ to any positive power yields $0$ .

$0 + 2 {(0)}^{2} + 0 < 2$

Step 2.1.2

Raising $0$ to any positive power yields $0$ .

$0 + 2 \cdot 0 + 0 < 2$

Step 2.1.3

Multiply $2$ by $0$ .

$0 + 0 + 0 < 2$

Step 2.2

Simplify by adding numbers.

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Step 2.2.1

Add $0$ and $0$ .

$0 + 0 < 2$

Step 2.2.2

Add $0$ and $0$ .

$0 < 2$

Step 3

Since $0 < 2$ , the inequality 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.

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Determine if (0,0) is a Solution

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