Finite Math Examples

$y = x^{2} + 6 x + 8$ , $y = x + 4$

Step 1

Eliminate the equal sides of each equation and combine.

$x^{2} + 6 x + 8 = x + 4$

Step 2

Solve $x^{2} + 6 x + 8 = x + 4$ for $x$ .

Tap for more steps...

Step 2.1

Move all terms containing $x$ to the left side of the equation.

Tap for more steps...

Step 2.1.1

Subtract $x$ from both sides of the equation.

$x^{2} + 6 x + 8 - x = 4$

Step 2.1.2

Subtract $x$ from $6 x$ .

$x^{2} + 5 x + 8 = 4$

Step 2.2

Subtract $4$ from both sides of the equation.

$x^{2} + 5 x + 8 - 4 = 0$

Step 2.3

Subtract $4$ from $8$ .

$x^{2} + 5 x + 4 = 0$

Step 2.4

Factor $x^{2} + 5 x + 4$ using the AC method.

Tap for more steps...

Step 2.4.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $4$ and whose sum is $5$ .

$1, 4 + y = x + 4$

Step 2.4.2

Write the factored form using these integers.

$(x + 1) (x + 4) = 0$

Step 2.5

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x + 1 = 0$

$x + 4 = 0 + y = x + 4$

Step 2.6

Set $x + 1$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 2.6.1

Set $x + 1$ equal to $0$ .

$x + 1 = 0$

Step 2.6.2

Subtract $1$ from both sides of the equation.

$x = - 1$

Step 2.7

Set $x + 4$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 2.7.1

Set $x + 4$ equal to $0$ .

$x + 4 = 0$

Step 2.7.2

Subtract $4$ from both sides of the equation.

$x = - 4$

Step 2.8

The final solution is all the values that make $(x + 1) (x + 4) = 0$ true.

$x = - 1, - 4$

Step 3

Evaluate $y$ when $x = - 1$ .

Tap for more steps...

Step 3.1

Substitute $- 1$ for $x$ .

$y = (- 1) + 4$

Step 3.2

Substitute $- 1$ for $x$ in $y = (- 1) + 4$ and solve for $y$ .

Tap for more steps...

Step 3.2.1

Remove parentheses.

$y = - 1 + 4$

Step 3.2.2

Remove parentheses.

$y = (- 1) + 4$

Step 3.2.3

Add $- 1$ and $4$ .

$y = 3$

Step 4

Evaluate $y$ when $x = - 4$ .

Tap for more steps...

Step 4.1

Substitute $- 4$ for $x$ .

$y = (- 4) + 4$

Step 4.2

Substitute $- 4$ for $x$ in $y = (- 4) + 4$ and solve for $y$ .

Tap for more steps...

Step 4.2.1

Remove parentheses.

$y = - 4 + 4$

Step 4.2.2

Remove parentheses.

$y = (- 4) + 4$

Step 4.2.3

Add $- 4$ and $4$ .

$y = 0$

Step 5

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

$(- 1, 3)$

$(- 4, 0)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 1, 3), (- 4, 0)$

Equation Form:

$x = - 1, y = 3$

$x = - 4, y = 0$

Step 7