Algebra Examples

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

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 $x$ .

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Step 2.1

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

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Step 2.1.1

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

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

Step 2.1.2

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

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Step 2.1.2.1

Subtract $3 x$ from $3 x$ .

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

Step 2.1.2.2

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

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

Step 2.2

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

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Step 2.2.1

Subtract $2$ from both sides of the equation.

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

Step 2.2.2

Subtract $2$ from $2$ .

$- x^{2} = 0$

Step 2.3

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

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Step 2.3.1

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

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

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Dividing two negative values results in a positive value.

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

Step 2.3.2.2

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

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

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $0$ by $- 1$ .

$x^{2} = 0$

Step 2.4

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

$x = \pm \sqrt{0}$

Step 2.5

Simplify $\pm \sqrt{0}$ .

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Step 2.5.1

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

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

Step 2.5.2

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

$x = \pm 0$

Step 2.5.3

Plus or minus $0$ is $0$ .

$x = 0$

Step 3

Evaluate $y$ when $x = 0$ .

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Step 3.1

Substitute $0$ for $x$ .

$y = 3 (0) + 2$

Step 3.2

Simplify $3 (0) + 2$ .

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Step 3.2.1

Multiply $3$ by $0$ .

$y = 0 + 2$

Step 3.2.2

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