Solve by Substitution y=-x^2-5x-4 , y=-x^2+9x-18

$y = - x^{2} - 5 x - 4$ , $y = - x^{2} + 9 x - 18$

Step 1

Eliminate the equal sides of each equation and combine.

$- x^{2} - 5 x - 4 = - x^{2} + 9 x - 18$

Step 2

Solve $- x^{2} - 5 x - 4 = - x^{2} + 9 x - 18$ for $x$ .

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

Add $x^{2}$ to both sides of the equation.

$- x^{2} - 5 x - 4 + x^{2} = 9 x - 18$

Subtract $9 x$ from both sides of the equation.

$- x^{2} - 5 x - 4 + x^{2} - 9 x = - 18$

Combine the opposite terms in $- x^{2} - 5 x - 4 + x^{2} - 9 x$ .

Add $- x^{2}$ and $x^{2}$ .

$- 5 x - 4 + 0 - 9 x = - 18$

Add $- 5 x - 4$ and $0$ .

$- 5 x - 4 - 9 x = - 18$

Subtract $9 x$ from $- 5 x$ .

$- 14 x - 4 = - 18$

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

Add $4$ to both sides of the equation.

$- 14 x = - 18 + 4$

Add $- 18$ and $4$ .

$- 14 x = - 14$

Divide each term in $- 14 x = - 14$ by $- 14$ and simplify.

Divide each term in $- 14 x = - 14$ by $- 14$ .

$\frac{- 14 x}{- 14} = \frac{- 14}{- 14}$

Simplify the left side.

Cancel the common factor of $- 14$ .

Cancel the common factor.

$\frac{- 14 x}{- 14} = \frac{- 14}{- 14}$

Divide $x$ by $1$ .

$x = \frac{- 14}{- 14}$

Simplify the right side.

Divide $- 14$ by $- 14$ .

$x = 1$

Step 3

Evaluate $y$ when $x = 1$ .

Substitute $1$ for $x$ .

$y = - {(1)}^{2} + 9 (1) - 18$

Substitute $1$ for $x$ in $y = - {(1)}^{2} + 9 (1) - 18$ and solve for $y$ .

Remove parentheses.

$y = - 1^{2} + 9 (1) - 18$

Simplify $- 1^{2} + 9 (1) - 18$ .

Simplify each term.

One to any power is one.

$y = - 1 \cdot 1 + 9 (1) - 18$

Multiply $- 1$ by $1$ .

$y = - 1 + 9 (1) - 18$

Multiply $9$ by $1$ .

$y = - 1 + 9 - 18$

Simplify by adding and subtracting.

Add $- 1$ and $9$ .

$y = 8 - 18$

Subtract $18$ from $8$ .

$y = - 10$

Step 4

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

$(1, - 10)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(1, - 10)$

Equation Form:

$x = 1, y = - 10$

Step 6

Solve by Substitution y=-x^2-5x-4 , y=-x^2+9x-18

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