Algebra Examples

$y = x^{2} + 3 x + 7$ $y = 11 x - 9$

Step 1

Eliminate the equal sides of each equation and combine.

$x^{2} + 3 x + 7 = 11 x - 9$

Step 2

Solve $x^{2} + 3 x + 7 = 11 x - 9$ 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 $11 x$ from both sides of the equation.

$x^{2} + 3 x + 7 - 11 x = - 9$

Step 2.1.2

Subtract $11 x$ from $3 x$ .

$x^{2} - 8 x + 7 = - 9$

Step 2.2

Add $9$ to both sides of the equation.

$x^{2} - 8 x + 7 + 9 = 0$

Step 2.3

Add $7$ and $9$ .

$x^{2} - 8 x + 16 = 0$

Step 2.4

Factor using the perfect square rule.

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Step 2.4.1

Rewrite $16$ as $4^{2}$ .

$x^{2} - 8 x + 4^{2} = 0$

Step 2.4.2

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

$8 x = 2 \cdot x \cdot 4$

Step 2.4.3

Rewrite the polynomial.

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

Step 2.4.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = x$ and $b = 4$ .

${(x - 4)}^{2} = 0$

Step 2.5

Set the $x - 4$ equal to $0$ .

$x - 4 = 0$

Step 2.6

Add $4$ to both sides of the equation.

$x = 4$

Step 3

Evaluate $y$ when $x = 4$ .

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Step 3.1

Substitute $4$ for $x$ .

$y = 11 (4) - 9$

Step 3.2

Simplify $11 (4) - 9$ .

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Step 3.2.1

Multiply $11$ by $4$ .

$y = 44 - 9$

Step 3.2.2

Subtract $9$ from $44$ .

$y = 35$

Step 4

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

$(4, 35)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(4, 35)$

Equation Form:

$x = 4, y = 35$

Step 6