Solve the System of Equations 3x-3y=-9 and -6x+8y=6

$3 x - 3 y = - 9$ and $- 6 x + 8 y = 6$

Step 1

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

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

$3 x = - 9 + 3 y$

$- 6 x + 8 y = 6$

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

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

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

$- 6 x + 8 y = 6$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

$- 6 x + 8 y = 6$

Divide $x$ by $1$ .

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

$- 6 x + 8 y = 6$

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

$- 6 x + 8 y = 6$

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

$- 6 x + 8 y = 6$

Simplify the right side.

Simplify each term.

Divide $- 9$ by $3$ .

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

$- 6 x + 8 y = 6$

Cancel the common factor of $3$ .

Cancel the common factor.

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

$- 6 x + 8 y = 6$

Divide $y$ by $1$ .

$x = - 3 + y$

$- 6 x + 8 y = 6$

$x = - 3 + y$

$- 6 x + 8 y = 6$

$x = - 3 + y$

$- 6 x + 8 y = 6$

$x = - 3 + y$

$- 6 x + 8 y = 6$

$x = - 3 + y$

$- 6 x + 8 y = 6$

$x = - 3 + y$

$- 6 x + 8 y = 6$

Step 2

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

Replace all occurrences of $x$ in $- 6 x + 8 y = 6$ with $- 3 + y$ .

$- 6 (- 3 + y) + 8 y = 6$

$x = - 3 + y$

Simplify the left side.

Simplify $- 6 (- 3 + y) + 8 y$ .

Simplify each term.

Apply the distributive property.

$- 6 \cdot - 3 - 6 y + 8 y = 6$

$x = - 3 + y$

Multiply $- 6$ by $- 3$ .

$18 - 6 y + 8 y = 6$

$x = - 3 + y$

$18 - 6 y + 8 y = 6$

$x = - 3 + y$

Add $- 6 y$ and $8 y$ .

$18 + 2 y = 6$

$x = - 3 + y$

$18 + 2 y = 6$

$x = - 3 + y$

$18 + 2 y = 6$

$x = - 3 + y$

$18 + 2 y = 6$

$x = - 3 + y$

Step 3

Solve for $y$ in $18 + 2 y = 6$ .

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

Subtract $18$ from both sides of the equation.

$2 y = 6 - 18$

$x = - 3 + y$

Subtract $18$ from $6$ .

$2 y = - 12$

$x = - 3 + y$

$2 y = - 12$

$x = - 3 + y$

Divide each term in $2 y = - 12$ by $2$ and simplify.

Divide each term in $2 y = - 12$ by $2$ .

$\frac{2 y}{2} = \frac{- 12}{2}$

$x = - 3 + y$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{- 12}{2}$

$x = - 3 + y$

Divide $y$ by $1$ .

$y = \frac{- 12}{2}$

$x = - 3 + y$

$y = \frac{- 12}{2}$

$x = - 3 + y$

$y = \frac{- 12}{2}$

$x = - 3 + y$

Simplify the right side.

Divide $- 12$ by $2$ .

$y = - 6$

$x = - 3 + y$

$y = - 6$

$x = - 3 + y$

$y = - 6$

$x = - 3 + y$

$y = - 6$

$x = - 3 + y$

Step 4

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

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

$x = - 3 - 6$

$y = - 6$

Simplify $x = - 3 - 6$ .

Simplify the left side.

Remove parentheses.

$x = - 3 - 6$

$y = - 6$

$x = - 3 - 6$

$y = - 6$

Simplify the right side.

Subtract $6$ from $- 3$ .

$x = - 9$

$y = - 6$

$x = - 9$

$y = - 6$

$x = - 9$

$y = - 6$

$x = - 9$

$y = - 6$

Step 5

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

$(- 9, - 6)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 9, - 6)$

Equation Form:

$x = - 9, y = - 6$

Step 7

Solve the System of Equations 3x-3y=-9 and -6x+8y=6

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