Solve the System of Equations y=x^2-7x-6 y=8-2x

$y = x^{2} - 7 x - 6$ $y = 8 - 2 x$

Step 1

Eliminate the equal sides of each equation and combine.

$x^{2} - 7 x - 6 = 8 - 2 x$

Step 2

Solve $x^{2} - 7 x - 6 = 8 - 2 x$ for $x$ .

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

Add $2 x$ to both sides of the equation.

$x^{2} - 7 x - 6 + 2 x = 8$

Add $- 7 x$ and $2 x$ .

$x^{2} - 5 x - 6 = 8$

Subtract $8$ from both sides of the equation.

$x^{2} - 5 x - 6 - 8 = 0$

Subtract $8$ from $- 6$ .

$x^{2} - 5 x - 14 = 0$

Factor $x^{2} - 5 x - 14$ 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 $- 14$ and whose sum is $- 5$ .

$- 7, 2 + y = 8 - 2 x$

Write the factored form using these integers.

$(x - 7) (x + 2) = 0$

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

$x - 7 = 0$

$x + 2 = 0 + y = 8 - 2 x$

Set $x - 7$ equal to $0$ and solve for $x$ .

Set $x - 7$ equal to $0$ .

$x - 7 = 0$

Add $7$ to both sides of the equation.

$x = 7$

Set $x + 2$ equal to $0$ and solve for $x$ .

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

The final solution is all the values that make $(x - 7) (x + 2) = 0$ true.

$x = 7, - 2$

Step 3

Evaluate $y$ when $x = 7$ .

Substitute $7$ for $x$ .

$y = 8 - 2 \cdot 7$

Substitute $7$ for $x$ in $y = 8 - 2 \cdot 7$ and solve for $y$ .

Remove parentheses.

$y = 8 - 2 \cdot 7$

Simplify $8 - 2 \cdot 7$ .

Multiply $- 2$ by $7$ .

$y = 8 - 14$

Subtract $14$ from $8$ .

$y = - 6$

Step 4

Evaluate $y$ when $x = - 2$ .

Substitute $- 2$ for $x$ .

$y = 8 - 2 \cdot - 2$

Substitute $- 2$ for $x$ in $y = 8 - 2 \cdot - 2$ and solve for $y$ .

Remove parentheses.

$y = 8 - 2 \cdot - 2$

Simplify $8 - 2 \cdot - 2$ .

Multiply $- 2$ by $- 2$ .

$y = 8 + 4$

Add $8$ and $4$ .

$y = 12$

Step 5

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

$(7, - 6)$

$(- 2, 12)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(7, - 6), (- 2, 12)$

Equation Form:

$x = 7, y = - 6$

$x = - 2, y = 12$

Step 7

Solve the System of Equations y=x^2-7x-6 y=8-2x

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