Examples

$x + 2 y = 4$ , $x - y = - 3$

Step 1

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

$x = 4 - 2 y$

$x - y = - 3$

Step 2

Replace all occurrences of $x$ with $4 - 2 y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $x - y = - 3$ with $4 - 2 y$ .

$(4 - 2 y) - y = - 3$

$x = 4 - 2 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Subtract $y$ from $- 2 y$ .

$4 - 3 y = - 3$

$x = 4 - 2 y$

$4 - 3 y = - 3$

$x = 4 - 2 y$

$4 - 3 y = - 3$

$x = 4 - 2 y$

Step 3

Solve for $y$ in $4 - 3 y = - 3$ .

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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 $4$ from both sides of the equation.

$- 3 y = - 3 - 4$

$x = 4 - 2 y$

Step 3.1.2

Subtract $4$ from $- 3$ .

$- 3 y = - 7$

$x = 4 - 2 y$

$- 3 y = - 7$

$x = 4 - 2 y$

Step 3.2

Divide each term in $- 3 y = - 7$ by $- 3$ and simplify.

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Step 3.2.1

Divide each term in $- 3 y = - 7$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 7}{- 3}$

$x = 4 - 2 y$

Step 3.2.2

Simplify the left side.

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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

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 7}{- 3}$

$x = 4 - 2 y$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 7}{- 3}$

$x = 4 - 2 y$

$y = \frac{- 7}{- 3}$

$x = 4 - 2 y$

$y = \frac{- 7}{- 3}$

$x = 4 - 2 y$

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.

$y = \frac{7}{3}$

$x = 4 - 2 y$

$y = \frac{7}{3}$

$x = 4 - 2 y$

$y = \frac{7}{3}$

$x = 4 - 2 y$

$y = \frac{7}{3}$

$x = 4 - 2 y$

Step 4

Replace all occurrences of $y$ with $\frac{7}{3}$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = 4 - 2 y$ with $\frac{7}{3}$ .

$x = 4 - 2 (\frac{7}{3})$

$y = \frac{7}{3}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $4 - 2 (\frac{7}{3})$ .

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Step 4.2.1.1

Simplify each term.

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Step 4.2.1.1.1

Multiply $- 2 (\frac{7}{3})$ .

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Step 4.2.1.1.1.1

Combine $- 2$ and $\frac{7}{3}$ .

$x = 4 + \frac{- 2 \cdot 7}{3}$

$y = \frac{7}{3}$

Step 4.2.1.1.1.2

Multiply $- 2$ by $7$ .

$x = 4 + \frac{- 14}{3}$

$y = \frac{7}{3}$

$x = 4 + \frac{- 14}{3}$

$y = \frac{7}{3}$

Step 4.2.1.1.2

Move the negative in front of the fraction.

$x = 4 - \frac{14}{3}$

$y = \frac{7}{3}$

$x = 4 - \frac{14}{3}$

$y = \frac{7}{3}$

Step 4.2.1.2

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

$x = 4 \cdot \frac{3}{3} - \frac{14}{3}$

$y = \frac{7}{3}$

Step 4.2.1.3

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

$x = \frac{4 \cdot 3}{3} - \frac{14}{3}$

$y = \frac{7}{3}$

Step 4.2.1.4

Combine the numerators over the common denominator.

$x = \frac{4 \cdot 3 - 14}{3}$

$y = \frac{7}{3}$

Step 4.2.1.5

Simplify the numerator.

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Step 4.2.1.5.1

Multiply $4$ by $3$ .

$x = \frac{12 - 14}{3}$

$y = \frac{7}{3}$

Step 4.2.1.5.2

Subtract $14$ from $12$ .

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

$y = \frac{7}{3}$

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

$y = \frac{7}{3}$

Step 4.2.1.6

Move the negative in front of the fraction.

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

$y = \frac{7}{3}$

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

$y = \frac{7}{3}$

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

$y = \frac{7}{3}$

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

$y = \frac{7}{3}$

Step 5

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

$(- \frac{2}{3}, \frac{7}{3})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- \frac{2}{3}, \frac{7}{3})$

Equation Form:

$x = - \frac{2}{3}, y = \frac{7}{3}$

Step 7

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