Solve the System of Equations y=x^2-16 y=x-4

$y = x^{2} - 16$ $y = x - 4$

Step 1

Eliminate the equal sides of each equation and combine.

$x^{2} - 16 = x - 4$

Step 2

Solve $x^{2} - 16 = x - 4$ for $x$ .

Subtract $x$ from both sides of the equation.

$x^{2} - 16 - x = - 4$

Add $4$ to both sides of the equation.

$x^{2} - 16 - x + 4 = 0$

Add $- 16$ and $4$ .

$x^{2} - x - 12 = 0$

Factor $x^{2} - x - 12$ using the AC method.

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 $- 12$ and whose sum is $- 1$ .

$- 4, 3 + y = x - 4$

Write the factored form using these integers.

$(x - 4) (x + 3) = 0$

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

$x - 4 = 0$

$x + 3 = 0 + y = x - 4$

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

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

$x - 4 = 0$

Add $4$ to both sides of the equation.

$x = 4$

Set $x + 3$ equal to $0$ and solve for $x$ .

Set $x + 3$ equal to $0$ .

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$

The final solution is all the values that make $(x - 4) (x + 3) = 0$ true.

$x = 4, - 3$

Step 3

Evaluate $y$ when $x = 4$ .

Substitute $4$ for $x$ .

$y = (4) - 4$

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

Remove parentheses.

$y = 4 - 4$

Remove parentheses.

$y = (4) - 4$

Subtract $4$ from $4$ .

$y = 0$

Step 4

Evaluate $y$ when $x = - 3$ .

Substitute $- 3$ for $x$ .

$y = (- 3) - 4$

Substitute $- 3$ for $x$ in $y = (- 3) - 4$ and solve for $y$ .

Remove parentheses.

$y = - 3 - 4$

Remove parentheses.

$y = (- 3) - 4$

Subtract $4$ from $- 3$ .

$y = - 7$

Step 5

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

$(4, 0)$

$(- 3, - 7)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(4, 0), (- 3, - 7)$

Equation Form:

$x = 4, y = 0$

$x = - 3, y = - 7$

Step 7

Solve the System of Equations y=x^2-16 y=x-4

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