Solve by Substitution y=x^2+10x+11 , y=x^2+x-7

$y = x^{2} + 10 x + 11$ , $y = x^{2} + x - 7$

Eliminate the equal sides of each equation and combine.

$x^{2} + 10 x + 11 = x^{2} + x - 7$

Solve $x^{2} + 10 x + 11 = x^{2} + x - 7$ for $x$ .

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

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Subtract $x^{2}$ from both sides of the equation.

$x^{2} + 10 x + 11 - x^{2} = x - 7$

Subtract $x$ from both sides of the equation.

$x^{2} + 10 x + 11 - x^{2} - x = - 7$

Combine the opposite terms in $x^{2} + 10 x + 11 - x^{2} - x$ .

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Subtract $x^{2}$ from $x^{2}$ .

$10 x + 11 + 0 - x = - 7$

Add $10 x + 11$ and $0$ .

$10 x + 11 - x = - 7$

Subtract $x$ from $10 x$ .

$9 x + 11 = - 7$

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

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Subtract $11$ from both sides of the equation.

$9 x = - 7 - 11$

Subtract $11$ from $- 7$ .

$9 x = - 18$

Divide each term by $9$ and simplify.

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Divide each term in $9 x = - 18$ by $9$ .

$\frac{9 x}{9} = \frac{- 18}{9}$

Cancel the common factor of $9$ .

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Cancel the common factor.

$\frac{9 x}{9} = \frac{- 18}{9}$

Divide $x$ by $1$ .

$x = \frac{- 18}{9}$

Divide $- 18$ by $9$ .

$x = - 2$

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

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Substitute $- 2$ for $x$ .

$y = {(- 2)}^{2} - 2 - 7$

Substitute $- 2$ for $x$ in $y = {(- 2)}^{2} - 2 - 7$ and solve for $y$ .

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Remove parentheses.

$y = {(- 2)}^{2} - 2 - 7$

Simplify ${(- 2)}^{2} - 2 - 7$ .

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Raise $- 2$ to the power of $2$ .

$y = 4 - 2 - 7$

Subtract $2$ from $4$ .

$y = 2 - 7$

Subtract $7$ from $2$ .

$y = - 5$

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

$(- 2, - 5)$

The result can be shown in multiple forms.

Point Form:

$(- 2, - 5)$

Equation Form:

$x = - 2, y = - 5$

Solve by Substitution y=x^2+10x+11 , y=x^2+x-7

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