Solve the System of Equations 3x+3=3y 2x-6y=2

$3 x + 3 = 3 y$ $2 x - 6 y = 2$

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

Subtract $3$ from both sides of the equation.

$3 x = 3 y - 3$

$2 x - 6 y = 2$

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

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

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

$2 x - 6 y = 2$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

$2 x - 6 y = 2$

Divide $x$ by $1$ .

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

$2 x - 6 y = 2$

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

$2 x - 6 y = 2$

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

$2 x - 6 y = 2$

Simplify the right side.

Simplify each term.

Cancel the common factor of $3$ .

Cancel the common factor.

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

$2 x - 6 y = 2$

Divide $y$ by $1$ .

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

$2 x - 6 y = 2$

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

$2 x - 6 y = 2$

Divide $- 3$ by $3$ .

$x = y - 1$

$2 x - 6 y = 2$

$x = y - 1$

$2 x - 6 y = 2$

$x = y - 1$

$2 x - 6 y = 2$

$x = y - 1$

$2 x - 6 y = 2$

$x = y - 1$

$2 x - 6 y = 2$

Replace all occurrences of $x$ with $y - 1$ in each equation.

Replace all occurrences of $x$ in $2 x - 6 y = 2$ with $y - 1$ .

$2 (y - 1) - 6 y = 2$

$x = y - 1$

Simplify the left side.

Simplify $2 (y - 1) - 6 y$ .

Simplify each term.

Apply the distributive property.

$2 y + 2 \cdot - 1 - 6 y = 2$

$x = y - 1$

Multiply $2$ by $- 1$ .

$2 y - 2 - 6 y = 2$

$x = y - 1$

$2 y - 2 - 6 y = 2$

$x = y - 1$

Subtract $6 y$ from $2 y$ .

$- 4 y - 2 = 2$

$x = y - 1$

$- 4 y - 2 = 2$

$x = y - 1$

$- 4 y - 2 = 2$

$x = y - 1$

$- 4 y - 2 = 2$

$x = y - 1$

Solve for $y$ in $- 4 y - 2 = 2$ .

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

Add $2$ to both sides of the equation.

$- 4 y = 2 + 2$

$x = y - 1$

Add $2$ and $2$ .

$- 4 y = 4$

$x = y - 1$

$- 4 y = 4$

$x = y - 1$

Divide each term in $- 4 y = 4$ by $- 4$ and simplify.

Divide each term in $- 4 y = 4$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{4}{- 4}$

$x = y - 1$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{4}{- 4}$

$x = y - 1$

Divide $y$ by $1$ .

$y = \frac{4}{- 4}$

$x = y - 1$

$y = \frac{4}{- 4}$

$x = y - 1$

$y = \frac{4}{- 4}$

$x = y - 1$

Simplify the right side.

Divide $4$ by $- 4$ .

$y = - 1$

$x = y - 1$

$y = - 1$

$x = y - 1$

$y = - 1$

$x = y - 1$

$y = - 1$

$x = y - 1$

Replace all occurrences of $y$ with $- 1$ in each equation.

Replace all occurrences of $y$ in $x = y - 1$ with $- 1$ .

$x = (- 1) - 1$

$y = - 1$

Simplify the right side.

Subtract $1$ from $- 1$ .

$x = - 2$

$y = - 1$

$x = - 2$

$y = - 1$

$x = - 2$

$y = - 1$

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

$(- 2, - 1)$

The result can be shown in multiple forms.

Point Form:

$(- 2, - 1)$

Equation Form:

$x = - 2, y = - 1$

Solve the System of Equations 3x+3=3y 2x-6y=2

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