Algebra Examples

$- 3 x + 3 y = 9$ and $2 x - 7 y = - 14$

Step 1

Solve for $x$ in $- 3 x + 3 y = 9$ .

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Step 1.1

Subtract $3 y$ from both sides of the equation.

$- 3 x = 9 - 3 y$

$2 x - 7 y = - 14$

Step 1.2

Divide each term in $- 3 x = 9 - 3 y$ by $- 3$ and simplify.

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Step 1.2.1

Divide each term in $- 3 x = 9 - 3 y$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{9}{- 3} + \frac{- 3 y}{- 3}$

$2 x - 7 y = - 14$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 3$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{9}{- 3} + \frac{- 3 y}{- 3}$

$2 x - 7 y = - 14$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{9}{- 3} + \frac{- 3 y}{- 3}$

$2 x - 7 y = - 14$

$x = \frac{9}{- 3} + \frac{- 3 y}{- 3}$

$2 x - 7 y = - 14$

$x = \frac{9}{- 3} + \frac{- 3 y}{- 3}$

$2 x - 7 y = - 14$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Divide $9$ by $- 3$ .

$x = - 3 + \frac{- 3 y}{- 3}$

$2 x - 7 y = - 14$

Step 1.2.3.1.2

Cancel the common factor of $- 3$ .

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Step 1.2.3.1.2.1

Cancel the common factor.

$x = - 3 + \frac{- 3 y}{- 3}$

$2 x - 7 y = - 14$

Step 1.2.3.1.2.2

Divide $y$ by $1$ .

$x = - 3 + y$

$2 x - 7 y = - 14$

$x = - 3 + y$

$2 x - 7 y = - 14$

$x = - 3 + y$

$2 x - 7 y = - 14$

$x = - 3 + y$

$2 x - 7 y = - 14$

$x = - 3 + y$

$2 x - 7 y = - 14$

$x = - 3 + y$

$2 x - 7 y = - 14$

Step 2

Replace all occurrences of $x$ with $- 3 + y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $2 x - 7 y = - 14$ with $- 3 + y$ .

$2 (- 3 + y) - 7 y = - 14$

$x = - 3 + y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $2 (- 3 + y) - 7 y$ .

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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.

$2 \cdot - 3 + 2 y - 7 y = - 14$

$x = - 3 + y$

Step 2.2.1.1.2

Multiply $2$ by $- 3$ .

$- 6 + 2 y - 7 y = - 14$

$x = - 3 + y$

$- 6 + 2 y - 7 y = - 14$

$x = - 3 + y$

Step 2.2.1.2

Subtract $7 y$ from $2 y$ .

$- 6 - 5 y = - 14$

$x = - 3 + y$

$- 6 - 5 y = - 14$

$x = - 3 + y$

$- 6 - 5 y = - 14$

$x = - 3 + y$

$- 6 - 5 y = - 14$

$x = - 3 + y$

Step 3

Solve for $y$ in $- 6 - 5 y = - 14$ .

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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

Add $6$ to both sides of the equation.

$- 5 y = - 14 + 6$

$x = - 3 + y$

Step 3.1.2

Add $- 14$ and $6$ .

$- 5 y = - 8$

$x = - 3 + y$

$- 5 y = - 8$

$x = - 3 + y$

Step 3.2

Divide each term in $- 5 y = - 8$ by $- 5$ and simplify.

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Step 3.2.1

Divide each term in $- 5 y = - 8$ by $- 5$ .

$\frac{- 5 y}{- 5} = \frac{- 8}{- 5}$

$x = - 3 + y$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 5$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 5 y}{- 5} = \frac{- 8}{- 5}$

$x = - 3 + y$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 8}{- 5}$

$x = - 3 + y$

$y = \frac{- 8}{- 5}$

$x = - 3 + y$

$y = \frac{- 8}{- 5}$

$x = - 3 + y$

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.

$y = \frac{8}{5}$

$x = - 3 + y$

$y = \frac{8}{5}$

$x = - 3 + y$

$y = \frac{8}{5}$

$x = - 3 + y$

$y = \frac{8}{5}$

$x = - 3 + y$

Step 4

Replace all occurrences of $y$ with $\frac{8}{5}$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = - 3 + y$ with $\frac{8}{5}$ .

$x = - 3 + \frac{8}{5}$

$y = \frac{8}{5}$

Step 4.2

Simplify $x = - 3 + \frac{8}{5}$ .

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Step 4.2.1

Simplify the left side.

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Step 4.2.1.1

Remove parentheses.

$x = - 3 + \frac{8}{5}$

$y = \frac{8}{5}$

$x = - 3 + \frac{8}{5}$

$y = \frac{8}{5}$

Step 4.2.2

Simplify the right side.

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Step 4.2.2.1

Simplify $- 3 + \frac{8}{5}$ .

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Step 4.2.2.1.1

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$x = - 3 \cdot \frac{5}{5} + \frac{8}{5}$

$y = \frac{8}{5}$

Step 4.2.2.1.2

Combine $- 3$ and $\frac{5}{5}$ .

$x = \frac{- 3 \cdot 5}{5} + \frac{8}{5}$

$y = \frac{8}{5}$

Step 4.2.2.1.3

Combine the numerators over the common denominator.

$x = \frac{- 3 \cdot 5 + 8}{5}$

$y = \frac{8}{5}$

Step 4.2.2.1.4

Simplify the numerator.

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Step 4.2.2.1.4.1

Multiply $- 3$ by $5$ .

$x = \frac{- 15 + 8}{5}$

$y = \frac{8}{5}$

Step 4.2.2.1.4.2

Add $- 15$ and $8$ .

$x = \frac{- 7}{5}$

$y = \frac{8}{5}$

$x = \frac{- 7}{5}$

$y = \frac{8}{5}$

Step 4.2.2.1.5

Move the negative in front of the fraction.

$x = - \frac{7}{5}$

$y = \frac{8}{5}$

$x = - \frac{7}{5}$

$y = \frac{8}{5}$

$x = - \frac{7}{5}$

$y = \frac{8}{5}$

$x = - \frac{7}{5}$

$y = \frac{8}{5}$

$x = - \frac{7}{5}$

$y = \frac{8}{5}$

Step 5

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

$(- \frac{7}{5}, \frac{8}{5})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- \frac{7}{5}, \frac{8}{5})$

Equation Form:

$x = - \frac{7}{5}, y = \frac{8}{5}$

Step 7