Algebra Examples

What is the solution to the system of equations $y = x^{2} - 2$ and $y = - 2$ ?

Step 1

Eliminate the equal sides of each equation and combine.

$x^{2} - 2 = - 2$

Step 2

Solve $x^{2} - 2 = - 2$ for $x$ .

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Step 2.1

Move all terms not containing $x$ to the right side of the equation.

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Step 2.1.1

Add $2$ to both sides of the equation.

$x^{2} = - 2 + 2$

Step 2.1.2

Add $- 2$ and $2$ .

$x^{2} = 0$

Step 2.2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{0}$

Step 2.3

Simplify $\pm \sqrt{0}$ .

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Step 2.3.1

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Step 2.3.2

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

Step 2.3.3

Plus or minus $0$ is $0$ .

$x = 0$

Step 3

Substitute $0$ for $x$ .

$y = - 2$

Step 4

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(0, - 2)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(0, - 2)$

Equation Form:

$x = 0, y = - 2$

Step 6