Algebra Examples

$8 x = 12$ $2 y + 10 = 22$

Step 1

Divide each term in $8 x = 12$ by $8$ and simplify.

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Step 1.1

Divide each term in $8 x = 12$ by $8$ .

$\frac{8 x}{8} = \frac{12}{8}$

$2 y + 10 = 22$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $8$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{8 x}{8} = \frac{12}{8}$

$2 y + 10 = 22$

Step 1.2.1.2

Divide $x$ by $1$ .

$x = \frac{12}{8}$

$2 y + 10 = 22$

$x = \frac{12}{8}$

$2 y + 10 = 22$

$x = \frac{12}{8}$

$2 y + 10 = 22$

Step 1.3

Simplify the right side.

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Step 1.3.1

Cancel the common factor of $12$ and $8$ .

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Step 1.3.1.1

Factor $4$ out of $12$ .

$x = \frac{4 (3)}{8}$

$2 y + 10 = 22$

Step 1.3.1.2

Cancel the common factors.

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Step 1.3.1.2.1

Factor $4$ out of $8$ .

$x = \frac{4 \cdot 3}{4 \cdot 2}$

$2 y + 10 = 22$

Step 1.3.1.2.2

Cancel the common factor.

$x = \frac{4 \cdot 3}{4 \cdot 2}$

$2 y + 10 = 22$

Step 1.3.1.2.3

Rewrite the expression.

$x = \frac{3}{2}$

$2 y + 10 = 22$

$x = \frac{3}{2}$

$2 y + 10 = 22$

$x = \frac{3}{2}$

$2 y + 10 = 22$

$x = \frac{3}{2}$

$2 y + 10 = 22$

$x = \frac{3}{2}$

$2 y + 10 = 22$

Step 2

Replace all occurrences of $x$ with $\frac{3}{2}$ in each equation.

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Step 2.1

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

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Step 2.1.1

Subtract $10$ from both sides of the equation.

$2 y = 22 - 10$

$x = \frac{3}{2}$

Step 2.1.2

Subtract $10$ from $22$ .

$2 y = 12$

$x = \frac{3}{2}$

$2 y = 12$

$x = \frac{3}{2}$

Step 2.2

Divide each term in $2 y = 12$ by $2$ and simplify.

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Step 2.2.1

Divide each term in $2 y = 12$ by $2$ .

$\frac{2 y}{2} = \frac{12}{2}$

$x = \frac{3}{2}$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $2$ .

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Step 2.2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{12}{2}$

$x = \frac{3}{2}$

Step 2.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{12}{2}$

$x = \frac{3}{2}$

$y = \frac{12}{2}$

$x = \frac{3}{2}$

$y = \frac{12}{2}$

$x = \frac{3}{2}$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Divide $12$ by $2$ .

$y = 6$

$x = \frac{3}{2}$

$y = 6$

$x = \frac{3}{2}$

$y = 6$

$x = \frac{3}{2}$

$y = 6$

$x = \frac{3}{2}$

Step 3

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

$(\frac{3}{2}, 6)$

Step 4

The result can be shown in multiple forms.

Point Form:

$(\frac{3}{2}, 6)$

Equation Form:

$x = \frac{3}{2}, y = 6$

Step 5