Algebra Examples

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

Step 1

Replace all occurrences of $y$ with $x^{2} - 2 x + 2$ in each equation.

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Step 1.1

Replace all occurrences of $y$ in $2 x + y = 2$ with $x^{2} - 2 x + 2$ .

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

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

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify $2 x + x^{2} - 2 x + 2$ .

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Step 1.2.1.1

Remove parentheses.

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

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

Step 1.2.1.2

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

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Step 1.2.1.2.1

Subtract $2 x$ from $2 x$ .

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

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

Step 1.2.1.2.2

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

$x^{2} + 2 = 2$

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

$x^{2} + 2 = 2$

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

$x^{2} + 2 = 2$

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

$x^{2} + 2 = 2$

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

$x^{2} + 2 = 2$

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

Step 2

Solve for $x$ in $x^{2} + 2 = 2$ .

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Step 2.1

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

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Step 2.1.1

Subtract $2$ from both sides of the equation.

$x^{2} = 2 - 2$

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

Step 2.1.2

Subtract $2$ from $2$ .

$x^{2} = 0$

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

$x^{2} = 0$

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

Step 2.2

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

$x = \pm \sqrt{0}$

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

Step 2.3

Simplify $\pm \sqrt{0}$ .

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Step 2.3.1

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

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

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

Step 2.3.2

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

$x = \pm 0$

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

Step 2.3.3

Plus or minus $0$ is $0$ .

$x = 0$

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

$x = 0$

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

$x = 0$

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

Step 3

Replace all occurrences of $x$ with $0$ in each equation.

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Step 3.1

Replace all occurrences of $x$ in $y = x^{2} - 2 x + 2$ with $0$ .

$y = {(0)}^{2} - 2 \cdot 0 + 2$

$x = 0$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify ${(0)}^{2} - 2 \cdot 0 + 2$ .

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Step 3.2.1.1

Simplify each term.

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Step 3.2.1.1.1

Raising $0$ to any positive power yields $0$ .

$y = 0 - 2 \cdot 0 + 2$

$x = 0$

Step 3.2.1.1.2

Multiply $- 2$ by $0$ .

$y = 0 + 0 + 2$

$x = 0$

$y = 0 + 0 + 2$

$x = 0$

Step 3.2.1.2

Simplify by adding numbers.

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Step 3.2.1.2.1

Add $0$ and $0$ .

$y = 0 + 2$

$x = 0$

Step 3.2.1.2.2

Add $0$ and $2$ .

$y = 2$

$x = 0$

$y = 2$

$x = 0$

$y = 2$

$x = 0$

$y = 2$

$x = 0$

$y = 2$

$x = 0$

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