Algebra Examples

$y = x^{2} + x + 9$ $3 x + y = 9$

Step 1

Replace all occurrences of $y$ with $x^{2} + x + 9$ in each equation.

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Step 1.1

Replace all occurrences of $y$ in $3 x + y = 9$ with $x^{2} + x + 9$ .

$3 x + x^{2} + x + 9 = 9$

$y = x^{2} + x + 9$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify $3 x + x^{2} + x + 9$ .

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Step 1.2.1.1

Remove parentheses.

$3 x + x^{2} + x + 9 = 9$

$y = x^{2} + x + 9$

Step 1.2.1.2

Add $3 x$ and $x$ .

$x^{2} + 4 x + 9 = 9$

$y = x^{2} + x + 9$

$x^{2} + 4 x + 9 = 9$

$y = x^{2} + x + 9$

$x^{2} + 4 x + 9 = 9$

$y = x^{2} + x + 9$

$x^{2} + 4 x + 9 = 9$

$y = x^{2} + x + 9$

Step 2

Solve for $x$ in $x^{2} + 4 x + 9 = 9$ .

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Step 2.1

Subtract $9$ from both sides of the equation.

$x^{2} + 4 x + 9 - 9 = 0$

$y = x^{2} + x + 9$

Step 2.2

Combine the opposite terms in $x^{2} + 4 x + 9 - 9$ .

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Step 2.2.1

Subtract $9$ from $9$ .

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

$y = x^{2} + x + 9$

Step 2.2.2

Add $x^{2} + 4 x$ and $0$ .

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

$y = x^{2} + x + 9$

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

$y = x^{2} + x + 9$

Step 2.3

Factor $x$ out of $x^{2} + 4 x$ .

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Step 2.3.1

Factor $x$ out of $x^{2}$ .

$x \cdot x + 4 x = 0$

$y = x^{2} + x + 9$

Step 2.3.2

Factor $x$ out of $4 x$ .

$x \cdot x + x \cdot 4 = 0$

$y = x^{2} + x + 9$

Step 2.3.3

Factor $x$ out of $x \cdot x + x \cdot 4$ .

$x (x + 4) = 0$

$y = x^{2} + x + 9$

$x (x + 4) = 0$

$y = x^{2} + x + 9$

Step 2.4

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$x + 4 = 0$

$y = x^{2} + x + 9$

Step 2.5

Set $x$ equal to $0$ .

$x = 0$

$y = x^{2} + x + 9$

Step 2.6

Set $x + 4$ equal to $0$ and solve for $x$ .

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Step 2.6.1

Set $x + 4$ equal to $0$ .

$x + 4 = 0$

$y = x^{2} + x + 9$

Step 2.6.2

Subtract $4$ from both sides of the equation.

$x = - 4$

$y = x^{2} + x + 9$

$x = - 4$

$y = x^{2} + x + 9$

Step 2.7

The final solution is all the values that make $x (x + 4) = 0$ true.

$x = 0, - 4$

$y = x^{2} + x + 9$

$x = 0, - 4$

$y = x^{2} + x + 9$

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 $y = x^{2} + x + 9$ with $0$ .

$y = {(0)}^{2} + 0 + 9$

$x = 0$

Step 3.2

Simplify $y = {(0)}^{2} + 0 + 9$ .

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Remove parentheses.

$y = {(0)}^{2} + 0 + 9$

$x = 0$

$y = {(0)}^{2} + 0 + 9$

$x = 0$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Simplify ${(0)}^{2} + 0 + 9$ .

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Step 3.2.2.1.1

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

$y = 0 + 0 + 9$

$x = 0$

Step 3.2.2.1.2

Add $0$ and $0$ .

$y = 0 + 9$

$x = 0$

Step 3.2.2.1.3

Add $0$ and $9$ .

$y = 9$

$x = 0$

$y = 9$

$x = 0$

$y = 9$

$x = 0$

$y = 9$

$x = 0$

$y = 9$

$x = 0$

Step 4

Replace all occurrences of $x$ with $- 4$ in each equation.

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Step 4.1

Replace all occurrences of $x$ in $y = x^{2} + x + 9$ with $- 4$ .

$y = {(- 4)}^{2} - 4 + 9$

$x = - 4$

Step 4.2

Simplify $y = {(- 4)}^{2} - 4 + 9$ .

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Step 4.2.1

Simplify the left side.

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Step 4.2.1.1

Remove parentheses.

$y = {(- 4)}^{2} - 4 + 9$

$x = - 4$

$y = {(- 4)}^{2} - 4 + 9$

$x = - 4$

Step 4.2.2

Simplify the right side.

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Step 4.2.2.1

Simplify ${(- 4)}^{2} - 4 + 9$ .

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Step 4.2.2.1.1

Raise $- 4$ to the power of $2$ .

$y = 16 - 4 + 9$

$x = - 4$

Step 4.2.2.1.2

Subtract $4$ from $16$ .

$y = 12 + 9$

$x = - 4$

Step 4.2.2.1.3

Add $12$ and $9$ .

$y = 21$

$x = - 4$

$y = 21$

$x = - 4$

$y = 21$

$x = - 4$

$y = 21$

$x = - 4$

$y = 21$

$x = - 4$

Step 5

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

$(0, 9)$

$(- 4, 21)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(0, 9), (- 4, 21)$

Equation Form:

$x = 0, y = 9$

$x = - 4, y = 21$

Step 7