Finite Math Examples

$y = x^{2} + 5$ , $y = | 6 |$

Step 1

Eliminate the equal sides of each equation and combine.

$x^{2} + 5 = | 6 |$

Step 2

Solve $x^{2} + 5 = | 6 |$ for $x$ .

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Step 2.1

The absolute value is the distance between a number and zero. The distance between $0$ and $6$ is $6$ .

$x^{2} + 5 = 6$

Step 2.2

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

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Step 2.2.1

Subtract $5$ from both sides of the equation.

$x^{2} = 6 - 5$

Step 2.2.2

Subtract $5$ from $6$ .

$x^{2} = 1$

Step 2.3

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

$x = \pm \sqrt{1}$

Step 2.4

Any root of $1$ is $1$ .

$x = \pm 1$

Step 2.5

The complete solution is the result of both the positive and negative portions of the solution.

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Step 2.5.1

First, use the positive value of the $\pm$ to find the first solution.

$x = 1$

Step 2.5.2

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 1$

Step 2.5.3

The complete solution is the result of both the positive and negative portions of the solution.

$x = 1, - 1$

Step 3

Evaluate $y$ when $x = 1$ .

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Step 3.1

Substitute $1$ for $x$ .

$y = | 6 |$

Step 3.2

The absolute value is the distance between a number and zero. The distance between $0$ and $6$ is $6$ .

$y = 6$

Step 4

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

$(1, 6)$

$(- 1, 6)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(1, 6), (- 1, 6)$

Equation Form:

$x = 1, y = 6$

$x = - 1, y = 6$

Step 6