Solve the System of Equations y=2x^2-5x+9 y=2x^2+5x-1

$y = 2 x^{2} - 5 x + 9$ $y = 2 x^{2} + 5 x - 1$

Step 1

Eliminate the equal sides of each equation and combine.

$2 x^{2} - 5 x + 9 = 2 x^{2} + 5 x - 1$

Step 2

Solve $2 x^{2} - 5 x + 9 = 2 x^{2} + 5 x - 1$ for $x$ .

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

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

$2 x^{2} - 5 x + 9 - 2 x^{2} = 5 x - 1$

Subtract $5 x$ from both sides of the equation.

$2 x^{2} - 5 x + 9 - 2 x^{2} - 5 x = - 1$

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

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

$- 5 x + 9 + 0 - 5 x = - 1$

Add $- 5 x + 9$ and $0$ .

$- 5 x + 9 - 5 x = - 1$

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

$- 10 x + 9 = - 1$

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

Subtract $9$ from both sides of the equation.

$- 10 x = - 1 - 9$

Subtract $9$ from $- 1$ .

$- 10 x = - 10$

Divide each term in $- 10 x = - 10$ by $- 10$ and simplify.

Divide each term in $- 10 x = - 10$ by $- 10$ .

$\frac{- 10 x}{- 10} = \frac{- 10}{- 10}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 x}{- 10} = \frac{- 10}{- 10}$

Divide $x$ by $1$ .

$x = \frac{- 10}{- 10}$

Simplify the right side.

Divide $- 10$ by $- 10$ .

$x = 1$

Step 3

Evaluate $y$ when $x = 1$ .

Substitute $1$ for $x$ .

$y = 2 {(1)}^{2} + 5 (1) - 1$

Substitute $1$ for $x$ in $y = 2 {(1)}^{2} + 5 (1) - 1$ and solve for $y$ .

Remove parentheses.

$y = 2 \cdot 1^{2} + 5 (1) - 1$

Simplify $2 \cdot 1^{2} + 5 (1) - 1$ .

Simplify each term.

One to any power is one.

$y = 2 \cdot 1 + 5 (1) - 1$

Multiply $2$ by $1$ .

$y = 2 + 5 (1) - 1$

Multiply $5$ by $1$ .

$y = 2 + 5 - 1$

Simplify by adding and subtracting.

Add $2$ and $5$ .

$y = 7 - 1$

Subtract $1$ from $7$ .

$y = 6$

Step 4

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

$(1, 6)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(1, 6)$

Equation Form:

$x = 1, y = 6$

Step 6

Solve the System of Equations y=2x^2-5x+9 y=2x^2+5x-1

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