Pre-Algebra Examples

$x + 2 y = 6$ , $3 x - y = - 6$

Step 1

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

$x = 6 - 2 y$

$3 x - y = - 6$

Step 2

Replace all occurrences of $x$ with $6 - 2 y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $3 x - y = - 6$ with $6 - 2 y$ .

$3 (6 - 2 y) - y = - 6$

$x = 6 - 2 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $3 (6 - 2 y) - y$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

$3 \cdot 6 + 3 (- 2 y) - y = - 6$

$x = 6 - 2 y$

Step 2.2.1.1.2

Multiply $3$ by $6$ .

$18 + 3 (- 2 y) - y = - 6$

$x = 6 - 2 y$

Step 2.2.1.1.3

Multiply $- 2$ by $3$ .

$18 - 6 y - y = - 6$

$x = 6 - 2 y$

$18 - 6 y - y = - 6$

$x = 6 - 2 y$

Step 2.2.1.2

Subtract $y$ from $- 6 y$ .

$18 - 7 y = - 6$

$x = 6 - 2 y$

$18 - 7 y = - 6$

$x = 6 - 2 y$

$18 - 7 y = - 6$

$x = 6 - 2 y$

$18 - 7 y = - 6$

$x = 6 - 2 y$

Step 3

Solve for $y$ in $18 - 7 y = - 6$ .

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Step 3.1

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

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Step 3.1.1

Subtract $18$ from both sides of the equation.

$- 7 y = - 6 - 18$

$x = 6 - 2 y$

Step 3.1.2

Subtract $18$ from $- 6$ .

$- 7 y = - 24$

$x = 6 - 2 y$

$- 7 y = - 24$

$x = 6 - 2 y$

Step 3.2

Divide each term in $- 7 y = - 24$ by $- 7$ and simplify.

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Step 3.2.1

Divide each term in $- 7 y = - 24$ by $- 7$ .

$\frac{- 7 y}{- 7} = \frac{- 24}{- 7}$

$x = 6 - 2 y$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 7$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{- 24}{- 7}$

$x = 6 - 2 y$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 24}{- 7}$

$x = 6 - 2 y$

$y = \frac{- 24}{- 7}$

$x = 6 - 2 y$

$y = \frac{- 24}{- 7}$

$x = 6 - 2 y$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Dividing two negative values results in a positive value.

$y = \frac{24}{7}$

$x = 6 - 2 y$

$y = \frac{24}{7}$

$x = 6 - 2 y$

$y = \frac{24}{7}$

$x = 6 - 2 y$

$y = \frac{24}{7}$

$x = 6 - 2 y$

Step 4

Replace all occurrences of $y$ with $\frac{24}{7}$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = 6 - 2 y$ with $\frac{24}{7}$ .

$x = 6 - 2 (\frac{24}{7})$

$y = \frac{24}{7}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $6 - 2 (\frac{24}{7})$ .

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Step 4.2.1.1

Simplify each term.

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Step 4.2.1.1.1

Multiply $- 2 (\frac{24}{7})$ .

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Step 4.2.1.1.1.1

Combine $- 2$ and $\frac{24}{7}$ .

$x = 6 + \frac{- 2 \cdot 24}{7}$

$y = \frac{24}{7}$

Step 4.2.1.1.1.2

Multiply $- 2$ by $24$ .

$x = 6 + \frac{- 48}{7}$

$y = \frac{24}{7}$

$x = 6 + \frac{- 48}{7}$

$y = \frac{24}{7}$

Step 4.2.1.1.2

Move the negative in front of the fraction.

$x = 6 - \frac{48}{7}$

$y = \frac{24}{7}$

$x = 6 - \frac{48}{7}$

$y = \frac{24}{7}$

Step 4.2.1.2

To write $6$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$x = 6 \cdot \frac{7}{7} - \frac{48}{7}$

$y = \frac{24}{7}$

Step 4.2.1.3

Combine $6$ and $\frac{7}{7}$ .

$x = \frac{6 \cdot 7}{7} - \frac{48}{7}$

$y = \frac{24}{7}$

Step 4.2.1.4

Combine the numerators over the common denominator.

$x = \frac{6 \cdot 7 - 48}{7}$

$y = \frac{24}{7}$

Step 4.2.1.5

Simplify the numerator.

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Step 4.2.1.5.1

Multiply $6$ by $7$ .

$x = \frac{42 - 48}{7}$

$y = \frac{24}{7}$

Step 4.2.1.5.2

Subtract $48$ from $42$ .

$x = \frac{- 6}{7}$

$y = \frac{24}{7}$

$x = \frac{- 6}{7}$

$y = \frac{24}{7}$

Step 4.2.1.6

Move the negative in front of the fraction.

$x = - \frac{6}{7}$

$y = \frac{24}{7}$

$x = - \frac{6}{7}$

$y = \frac{24}{7}$

$x = - \frac{6}{7}$

$y = \frac{24}{7}$

$x = - \frac{6}{7}$

$y = \frac{24}{7}$

Step 5

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

$(- \frac{6}{7}, \frac{24}{7})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- \frac{6}{7}, \frac{24}{7})$

Equation Form:

$x = - \frac{6}{7}, y = \frac{24}{7}$

Step 7