Solve by Substitution x-3y=3 2x=3y

$x - 3 y = 3$ $2 x = 3 y$

Step 1

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

$x = 3 + 3 y$

$2 x = 3 y$

Step 2

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

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

$2 (3 + 3 y) = 3 y$

$x = 3 + 3 y$

Simplify the left side.

Simplify $2 (3 + 3 y)$ .

Apply the distributive property.

$2 \cdot 3 + 2 (3 y) = 3 y$

$x = 3 + 3 y$

Multiply.

Multiply $2$ by $3$ .

$6 + 2 (3 y) = 3 y$

$x = 3 + 3 y$

Multiply $3$ by $2$ .

$6 + 6 y = 3 y$

$x = 3 + 3 y$

$6 + 6 y = 3 y$

$x = 3 + 3 y$

$6 + 6 y = 3 y$

$x = 3 + 3 y$

$6 + 6 y = 3 y$

$x = 3 + 3 y$

$6 + 6 y = 3 y$

$x = 3 + 3 y$

Step 3

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

Move all terms containing $y$ to the left side of the equation.

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

$6 + 6 y - 3 y = 0$

$x = 3 + 3 y$

Subtract $3 y$ from $6 y$ .

$6 + 3 y = 0$

$x = 3 + 3 y$

$6 + 3 y = 0$

$x = 3 + 3 y$

Subtract $6$ from both sides of the equation.

$3 y = - 6$

$x = 3 + 3 y$

Divide each term in $3 y = - 6$ by $3$ and simplify.

Divide each term in $3 y = - 6$ by $3$ .

$\frac{3 y}{3} = \frac{- 6}{3}$

$x = 3 + 3 y$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 6}{3}$

$x = 3 + 3 y$

Divide $y$ by $1$ .

$y = \frac{- 6}{3}$

$x = 3 + 3 y$

$y = \frac{- 6}{3}$

$x = 3 + 3 y$

$y = \frac{- 6}{3}$

$x = 3 + 3 y$

Simplify the right side.

Divide $- 6$ by $3$ .

$y = - 2$

$x = 3 + 3 y$

$y = - 2$

$x = 3 + 3 y$

$y = - 2$

$x = 3 + 3 y$

$y = - 2$

$x = 3 + 3 y$

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 $- 2$ .

$x = 3 - 6$

$y = - 2$

Subtract $6$ from $3$ .

$x = - 3$

$y = - 2$

$x = - 3$

$y = - 2$

$x = - 3$

$y = - 2$

$x = - 3$

$y = - 2$

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 by Substitution x-3y=3 2x=3y

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