Solve the System of Equations y=x^2+10x y=x-8

$y = x^{2} + 10 x$ $y = x - 8$

Step 1

Eliminate the equal sides of each equation and combine.

$x^{2} + 10 x = x - 8$

Step 2

Solve $x^{2} + 10 x = x - 8$ for $x$ .

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

Subtract $x$ from both sides of the equation.

$x^{2} + 10 x - x = - 8$

Subtract $x$ from $10 x$ .

$x^{2} + 9 x = - 8$

Add $8$ to both sides of the equation.

$x^{2} + 9 x + 8 = 0$

Factor $x^{2} + 9 x + 8$ 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 $8$ and whose sum is $9$ .

$1, 8 + y = x - 8$

Write the factored form using these integers.

$(x + 1) (x + 8) = 0$

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

$x + 1 = 0$

$x + 8 = 0 + y = x - 8$

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

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

$x + 1 = 0$

Subtract $1$ from both sides of the equation.

$x = - 1$

Set $x + 8$ equal to $0$ and solve for $x$ .

Set $x + 8$ equal to $0$ .

$x + 8 = 0$

Subtract $8$ from both sides of the equation.

$x = - 8$

The final solution is all the values that make $(x + 1) (x + 8) = 0$ true.

$x = - 1, - 8$

Step 3

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

Substitute $- 1$ for $x$ .

$y = (- 1) - 8$

Substitute $- 1$ for $x$ in $y = (- 1) - 8$ and solve for $y$ .

Remove parentheses.

$y = - 1 - 8$

Remove parentheses.

$y = (- 1) - 8$

Subtract $8$ from $- 1$ .

$y = - 9$

Step 4

Evaluate $y$ when $x = - 8$ .

Substitute $- 8$ for $x$ .

$y = (- 8) - 8$

Substitute $- 8$ for $x$ in $y = (- 8) - 8$ and solve for $y$ .

Remove parentheses.

$y = - 8 - 8$

Remove parentheses.

$y = (- 8) - 8$

Subtract $8$ from $- 8$ .

$y = - 16$

Step 5

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

$(- 1, - 9)$

$(- 8, - 16)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 1, - 9), (- 8, - 16)$

Equation Form:

$x = - 1, y = - 9$

$x = - 8, y = - 16$

Step 7

Solve the System of Equations y=x^2+10x y=x-8

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