Algebra Examples

$y = \frac{3}{4} x + 12$ $y = \frac{4}{3} x$

Step 1

Eliminate the equal sides of each equation and combine.

$\frac{3}{4} x + 12 = \frac{4}{3} x$

Step 2

Solve $\frac{3}{4} x + 12 = \frac{4}{3} x$ for $x$ .

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Step 2.1

Combine $\frac{3}{4}$ and $x$ .

$\frac{3 x}{4} + 12 = \frac{4}{3} x$

Step 2.2

Combine $\frac{4}{3}$ and $x$ .

$\frac{3 x}{4} + 12 = \frac{4 x}{3}$

Step 2.3

Move all terms containing $x$ to the left side of the equation.

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Step 2.3.1

Subtract $\frac{4 x}{3}$ from both sides of the equation.

$\frac{3 x}{4} + 12 - \frac{4 x}{3} = 0$

Step 2.3.2

To write $\frac{3 x}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3 x}{4} \cdot \frac{3}{3} - \frac{4 x}{3} + 12 = 0$

Step 2.3.3

To write $- \frac{4 x}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{3 x}{4} \cdot \frac{3}{3} - \frac{4 x}{3} \cdot \frac{4}{4} + 12 = 0$

Step 2.3.4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.4.1

Multiply $\frac{3 x}{4}$ by $\frac{3}{3}$ .

$\frac{3 x \cdot 3}{4 \cdot 3} - \frac{4 x}{3} \cdot \frac{4}{4} + 12 = 0$

Step 2.3.4.2

Multiply $4$ by $3$ .

$\frac{3 x \cdot 3}{12} - \frac{4 x}{3} \cdot \frac{4}{4} + 12 = 0$

Step 2.3.4.3

Multiply $\frac{4 x}{3}$ by $\frac{4}{4}$ .

$\frac{3 x \cdot 3}{12} - \frac{4 x \cdot 4}{3 \cdot 4} + 12 = 0$

Step 2.3.4.4

Multiply $3$ by $4$ .

$\frac{3 x \cdot 3}{12} - \frac{4 x \cdot 4}{12} + 12 = 0$

Step 2.3.5

Combine the numerators over the common denominator.

$\frac{3 x \cdot 3 - 4 x \cdot 4}{12} + 12 = 0$

Step 2.3.6

Simplify each term.

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Step 2.3.6.1

Simplify the numerator.

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Step 2.3.6.1.1

Factor $x$ out of $3 x \cdot 3 - 4 x \cdot 4$ .

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Step 2.3.6.1.1.1

Factor $x$ out of $3 x \cdot 3$ .

$\frac{x (3 \cdot 3) - 4 x \cdot 4}{12} + 12 = 0$

Step 2.3.6.1.1.2

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

$\frac{x (3 \cdot 3) + x (- 4 \cdot 4)}{12} + 12 = 0$

Step 2.3.6.1.1.3

Factor $x$ out of $x (3 \cdot 3) + x (- 4 \cdot 4)$ .

$\frac{x (3 \cdot 3 - 4 \cdot 4)}{12} + 12 = 0$

Step 2.3.6.1.2

Multiply $3$ by $3$ .

$\frac{x (9 - 4 \cdot 4)}{12} + 12 = 0$

Step 2.3.6.1.3

Multiply $- 4$ by $4$ .

$\frac{x (9 - 16)}{12} + 12 = 0$

Step 2.3.6.1.4

Subtract $16$ from $9$ .

$\frac{x \cdot - 7}{12} + 12 = 0$

Step 2.3.6.2

Move $- 7$ to the left of $x$ .

$\frac{- 7 \cdot x}{12} + 12 = 0$

Step 2.3.6.3

Move the negative in front of the fraction.

$- \frac{7 x}{12} + 12 = 0$

Step 2.4

Subtract $12$ from both sides of the equation.

$- \frac{7 x}{12} = - 12$

Step 2.5

Multiply both sides of the equation by $- \frac{12}{7}$ .

$- \frac{12}{7} (- \frac{7 x}{12}) = - \frac{12}{7} \cdot - 12$

Step 2.6

Simplify both sides of the equation.

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Step 2.6.1

Simplify the left side.

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Step 2.6.1.1

Simplify $- \frac{12}{7} (- \frac{7 x}{12})$ .

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Step 2.6.1.1.1

Cancel the common factor of $12$ .

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Step 2.6.1.1.1.1

Move the leading negative in $- \frac{12}{7}$ into the numerator.

$\frac{- 12}{7} (- \frac{7 x}{12}) = - \frac{12}{7} \cdot - 12$

Step 2.6.1.1.1.2

Move the leading negative in $- \frac{7 x}{12}$ into the numerator.

$\frac{- 12}{7} \cdot \frac{- 7 x}{12} = - \frac{12}{7} \cdot - 12$

Step 2.6.1.1.1.3

Factor $12$ out of $- 12$ .

$\frac{12 (- 1)}{7} \cdot \frac{- 7 x}{12} = - \frac{12}{7} \cdot - 12$

Step 2.6.1.1.1.4

Cancel the common factor.

$\frac{12 \cdot - 1}{7} \cdot \frac{- 7 x}{12} = - \frac{12}{7} \cdot - 12$

Step 2.6.1.1.1.5

Rewrite the expression.

$\frac{- 1}{7} (- 7 x) = - \frac{12}{7} \cdot - 12$

Step 2.6.1.1.2

Cancel the common factor of $7$ .

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Step 2.6.1.1.2.1

Factor $7$ out of $- 7 x$ .

$\frac{- 1}{7} (7 (- x)) = - \frac{12}{7} \cdot - 12$

Step 2.6.1.1.2.2

Cancel the common factor.

$\frac{- 1}{7} (7 (- x)) = - \frac{12}{7} \cdot - 12$

Step 2.6.1.1.2.3

Rewrite the expression.

$- - x = - \frac{12}{7} \cdot - 12$

Step 2.6.1.1.3

Multiply.

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Step 2.6.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{12}{7} \cdot - 12$

Step 2.6.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{12}{7} \cdot - 12$

Step 2.6.2

Simplify the right side.

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Step 2.6.2.1

Multiply $- \frac{12}{7} \cdot - 12$ .

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Step 2.6.2.1.1

Multiply $- 12$ by $- 1$ .

$x = 12 (\frac{12}{7})$

Step 2.6.2.1.2

Combine $12$ and $\frac{12}{7}$ .

$x = \frac{12 \cdot 12}{7}$

Step 2.6.2.1.3

Multiply $12$ by $12$ .

$x = \frac{144}{7}$

Step 3

Evaluate $y$ when $x = \frac{144}{7}$ .

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Step 3.1

Substitute $\frac{144}{7}$ for $x$ .

$y = \frac{4}{3} \cdot (\frac{144}{7})$

Step 3.2

Substitute $\frac{144}{7}$ for $x$ in $y = \frac{4}{3} \cdot (\frac{144}{7})$ and solve for $y$ .

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Step 3.2.1

Multiply $\frac{4}{3}$ by $\frac{144}{7}$ .

$y = \frac{4}{3} \cdot \frac{144}{7}$

Step 3.2.2

Simplify $\frac{4}{3} \cdot \frac{144}{7}$ .

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Step 3.2.2.1

Cancel the common factor of $3$ .

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Step 3.2.2.1.1

Factor $3$ out of $144$ .

$y = \frac{4}{3} \cdot \frac{3 (48)}{7}$

Step 3.2.2.1.2

Cancel the common factor.

$y = \frac{4}{3} \cdot \frac{3 \cdot 48}{7}$

Step 3.2.2.1.3

Rewrite the expression.

$y = 4 \cdot \frac{48}{7}$

Step 3.2.2.2

Combine $4$ and $\frac{48}{7}$ .

$y = \frac{4 \cdot 48}{7}$

Step 3.2.2.3

Multiply $4$ by $48$ .

$y = \frac{192}{7}$

Step 4

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

$(\frac{144}{7}, \frac{192}{7})$

Step 5

The result can be shown in multiple forms.

Point Form:

$(\frac{144}{7}, \frac{192}{7})$

Equation Form:

$x = \frac{144}{7}, y = \frac{192}{7}$

Step 6