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

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

Step 1

Add $3 y$ to both sides of the equation.

$x = - 3 + 3 y$

$x + 3 y = 9$

Step 2

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

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

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

$x = - 3 + 3 y$

Simplify the left side.

Add $3 y$ and $3 y$ .

$- 3 + 6 y = 9$

$x = - 3 + 3 y$

$- 3 + 6 y = 9$

$x = - 3 + 3 y$

$- 3 + 6 y = 9$

$x = - 3 + 3 y$

Step 3

Solve for $y$ in $- 3 + 6 y = 9$ .

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

Add $3$ to both sides of the equation.

$6 y = 9 + 3$

$x = - 3 + 3 y$

Add $9$ and $3$ .

$6 y = 12$

$x = - 3 + 3 y$

$6 y = 12$

$x = - 3 + 3 y$

Divide each term in $6 y = 12$ by $6$ and simplify.

Divide each term in $6 y = 12$ by $6$ .

$\frac{6 y}{6} = \frac{12}{6}$

$x = - 3 + 3 y$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} = \frac{12}{6}$

$x = - 3 + 3 y$

Divide $y$ by $1$ .

$y = \frac{12}{6}$

$x = - 3 + 3 y$

$y = \frac{12}{6}$

$x = - 3 + 3 y$

$y = \frac{12}{6}$

$x = - 3 + 3 y$

Simplify the right side.

Divide $12$ by $6$ .

$y = 2$

$x = - 3 + 3 y$

$y = 2$

$x = - 3 + 3 y$

$y = 2$

$x = - 3 + 3 y$

$y = 2$

$x = - 3 + 3 y$

Step 4

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

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

$x = - 3 + 3 (2)$

$y = 2$

Simplify the right side.

Simplify $- 3 + 3 (2)$ .

Multiply $3$ by $2$ .

$x = - 3 + 6$

$y = 2$

Add $- 3$ and $6$ .

$x = 3$

$y = 2$

$x = 3$

$y = 2$

$x = 3$

$y = 2$

$x = 3$

$y = 2$

Step 5

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

$(3, 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(3, 2)$

Equation Form:

$x = 3, y = 2$

Step 7

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

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