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Precalculus Examples Systems of Equations

Determine if (3,4) is a Solution

$x^{2} + y = 0$ , $y = 5 x^{2}$ , $(3, 4)$

Step 1

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

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Step 1.1

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

$9 + 4 = 0$

$4 = 5 {(3)}^{2}$

Step 1.2

Add $9$ and $4$ .

$13 = 0$

$4 = 5 {(3)}^{2}$

$13 = 0$

$4 = 5 {(3)}^{2}$

Step 2

Since $13 \neq 0$ , there are no solutions.

No solution

Step 3

Simplify $5 \cdot 3^{2}$ .

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Step 3.1

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

$4 = 5 \cdot 9$

No solution

Step 3.2

Multiply $5$ by $9$ .

$4 = 45$

No solution

Step 4

Since $4 \neq 45$ , there are no solutions.

No solution

Step 5

The ordered pair is not a solution to the system of equations.

$(3, 4)$ is not a solution

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Systems of Equations

More step-by-step Precalculus examples from this chapter.

Substitution Method Addition/Elimination Method Determining Parallel Lines Determining Perpendicular Lines Graphing Method Finding the Constant of Variation Dependent, Independent, and Inconsistent Systems Finding the Intersection (and) Finding the Union (or) Finding the Equation with Real Coefficients Solving in Terms of the Arbitrary Variable Finding a Direct Variation Equation

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$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$