Solve the System of Equations Solve x+3y=9 3x-3y=-13

Solve $x + 3 y = 9$ $3 x - 3 y = - 13$

Step 1

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

$x = 9 - 3 y$

$3 x - 3 y = - 13$

Step 2

Replace all occurrences of $x$ with $9 - 3 y$ in each equation.

Replace all occurrences of $x$ in $3 x - 3 y = - 13$ with $9 - 3 y$ .

$3 (9 - 3 y) - 3 y = - 13$

$x = 9 - 3 y$

Simplify the left side.

Simplify $3 (9 - 3 y) - 3 y$ .

Simplify each term.

Apply the distributive property.

$3 \cdot 9 + 3 (- 3 y) - 3 y = - 13$

$x = 9 - 3 y$

Multiply $3$ by $9$ .

$27 + 3 (- 3 y) - 3 y = - 13$

$x = 9 - 3 y$

Multiply $- 3$ by $3$ .

$27 - 9 y - 3 y = - 13$

$x = 9 - 3 y$

$27 - 9 y - 3 y = - 13$

$x = 9 - 3 y$

Subtract $3 y$ from $- 9 y$ .

$27 - 12 y = - 13$

$x = 9 - 3 y$

$27 - 12 y = - 13$

$x = 9 - 3 y$

$27 - 12 y = - 13$

$x = 9 - 3 y$

$27 - 12 y = - 13$

$x = 9 - 3 y$

Step 3

Solve for $y$ in $27 - 12 y = - 13$ .

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

Subtract $27$ from both sides of the equation.

$- 12 y = - 13 - 27$

$x = 9 - 3 y$

Subtract $27$ from $- 13$ .

$- 12 y = - 40$

$x = 9 - 3 y$

$- 12 y = - 40$

$x = 9 - 3 y$

Divide each term in $- 12 y = - 40$ by $- 12$ and simplify.

Divide each term in $- 12 y = - 40$ by $- 12$ .

$\frac{- 12 y}{- 12} = \frac{- 40}{- 12}$

$x = 9 - 3 y$

Simplify the left side.

Cancel the common factor of $- 12$ .

Cancel the common factor.

$\frac{- 12 y}{- 12} = \frac{- 40}{- 12}$

$x = 9 - 3 y$

Divide $y$ by $1$ .

$y = \frac{- 40}{- 12}$

$x = 9 - 3 y$

$y = \frac{- 40}{- 12}$

$x = 9 - 3 y$

$y = \frac{- 40}{- 12}$

$x = 9 - 3 y$

Simplify the right side.

Cancel the common factor of $- 40$ and $- 12$ .

Factor $- 4$ out of $- 40$ .

$y = \frac{- 4 \cdot 10}{- 12}$

$x = 9 - 3 y$

Cancel the common factors.

Factor $- 4$ out of $- 12$ .

$y = \frac{- 4 \cdot 10}{- 4 \cdot 3}$

$x = 9 - 3 y$

Cancel the common factor.

$y = \frac{- 4 \cdot 10}{- 4 \cdot 3}$

$x = 9 - 3 y$

Rewrite the expression.

$y = \frac{10}{3}$

$x = 9 - 3 y$

$y = \frac{10}{3}$

$x = 9 - 3 y$

$y = \frac{10}{3}$

$x = 9 - 3 y$

$y = \frac{10}{3}$

$x = 9 - 3 y$

$y = \frac{10}{3}$

$x = 9 - 3 y$

$y = \frac{10}{3}$

$x = 9 - 3 y$

Step 4

Replace all occurrences of $y$ with $\frac{10}{3}$ in each equation.

Replace all occurrences of $y$ in $x = 9 - 3 y$ with $\frac{10}{3}$ .

$x = 9 - 3 (\frac{10}{3})$

$y = \frac{10}{3}$

Simplify the right side.

Simplify $9 - 3 (\frac{10}{3})$ .

Simplify each term.

Cancel the common factor of $3$ .

Factor $3$ out of $- 3$ .

$x = 9 + 3 (- 1) (\frac{10}{3})$

$y = \frac{10}{3}$

Cancel the common factor.

$x = 9 + 3 \cdot (- 1 (\frac{10}{3}))$

$y = \frac{10}{3}$

Rewrite the expression.

$x = 9 - 1 \cdot 10$

$y = \frac{10}{3}$

$x = 9 - 1 \cdot 10$

$y = \frac{10}{3}$

Multiply $- 1$ by $10$ .

$x = 9 - 10$

$y = \frac{10}{3}$

$x = 9 - 10$

$y = \frac{10}{3}$

Subtract $10$ from $9$ .

$x = - 1$

$y = \frac{10}{3}$

$x = - 1$

$y = \frac{10}{3}$

$x = - 1$

$y = \frac{10}{3}$

$x = - 1$

$y = \frac{10}{3}$

Step 5

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

$(- 1, \frac{10}{3})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 1, \frac{10}{3})$

Equation Form:

$x = - 1, y = \frac{10}{3}$

Step 7

Solve the System of Equations Solve x+3y=9 3x-3y=-13

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