Finite Math Examples

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

Step 1

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

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Step 1.1

Subtract $2 x$ from both sides of the equation.

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

$y - 2 x = - 2$

Step 1.2

Add $2$ to both sides of the equation.

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

$y - 2 x = - 2$

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

$y - 2 x = - 2$

Step 2

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

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Step 2.1

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

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Subtract $2 x$ from $- 2 x$ .

$x^{2} - 4 x + 2 = - 2$

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

$x^{2} - 4 x + 2 = - 2$

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

$x^{2} - 4 x + 2 = - 2$

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

Step 3

Solve for $x$ in $x^{2} - 4 x + 2 = - 2$ .

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Step 3.1

Add $2$ to both sides of the equation.

$x^{2} - 4 x + 2 + 2 = 0$

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

Step 3.2

Add $2$ and $2$ .

$x^{2} - 4 x + 4 = 0$

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

Step 3.3

Factor using the perfect square rule.

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Step 3.3.1

Rewrite $4$ as $2^{2}$ .

$x^{2} - 4 x + 2^{2} = 0$

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

Step 3.3.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$4 x = 2 \cdot x \cdot 2$

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

Step 3.3.3

Rewrite the polynomial.

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

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

Step 3.3.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 2$ .

${(x - 2)}^{2} = 0$

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

${(x - 2)}^{2} = 0$

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

Step 3.4

Set the $x - 2$ equal to $0$ .

$x - 2 = 0$

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

Step 3.5

Add $2$ to both sides of the equation.

$x = 2$

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

$x = 2$

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

Step 4

Replace all occurrences of $x$ with $2$ in each equation.

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Step 4.1

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

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

$x = 2$

Step 4.2

Simplify the right side.

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Step 4.2.1

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

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Step 4.2.1.1

Simplify each term.

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Step 4.2.1.1.1

Raise $2$ to the power of $2$ .

$y = 4 - 2 \cdot 2 + 2$

$x = 2$

Step 4.2.1.1.2

Multiply $- 2$ by $2$ .

$y = 4 - 4 + 2$

$x = 2$

$y = 4 - 4 + 2$

$x = 2$

Step 4.2.1.2

Simplify by adding and subtracting.

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Step 4.2.1.2.1

Subtract $4$ from $4$ .

$y = 0 + 2$

$x = 2$

Step 4.2.1.2.2

Add $0$ and $2$ .

$y = 2$

$x = 2$

$y = 2$

$x = 2$

$y = 2$

$x = 2$

$y = 2$

$x = 2$

$y = 2$

$x = 2$

Step 5

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

$(2, 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(2, 2)$

Equation Form:

$x = 2, y = 2$

Step 7