Solve the System of Equations y=-x^2+3x+2 y=3x+2

$y = - x^{2} + 3 x + 2$ $y = 3 x + 2$

Step 1

Eliminate the equal sides of each equation and combine.

$- x^{2} + 3 x + 2 = 3 x + 2$

Step 2

Solve $- x^{2} + 3 x + 2 = 3 x + 2$ for $x$ .

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

Subtract $3 x$ from both sides of the equation.

$- x^{2} + 3 x + 2 - 3 x = 2$

Combine the opposite terms in $- x^{2} + 3 x + 2 - 3 x$ .

Subtract $3 x$ from $3 x$ .

$- x^{2} + 0 + 2 = 2$

Add $- x^{2}$ and $0$ .

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

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

Subtract $2$ from both sides of the equation.

$- x^{2} = 2 - 2$

Subtract $2$ from $2$ .

$- x^{2} = 0$

Divide each term in $- x^{2} = 0$ by $- 1$ and simplify.

Divide each term in $- x^{2} = 0$ by $- 1$ .

$\frac{- x^{2}}{- 1} = \frac{0}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x^{2}}{1} = \frac{0}{- 1}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{0}{- 1}$

Simplify the right side.

Divide $0$ by $- 1$ .

$x^{2} = 0$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{0}$

Simplify $\pm \sqrt{0}$ .

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

Plus or minus $0$ is $0$ .

$x = 0$

Step 3

Evaluate $y$ when $x = 0$ .

Substitute $0$ for $x$ .

$y = 3 (0) + 2$

Simplify $3 (0) + 2$ .

Multiply $3$ by $0$ .

$y = 0 + 2$

Add $0$ and $2$ .

$y = 2$

Step 4

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

$(0, 2)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(0, 2)$

Equation Form:

$x = 0, y = 2$

Step 6

Solve the System of Equations y=-x^2+3x+2 y=3x+2

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