Solve by Substitution 2x-3y=3 , -4x+6y=-6

$2 x - 3 y = 3$ , $- 4 x + 6 y = - 6$

Step 1

Solve for $x$ in $2 x - 3 y = 3$ .

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

$2 x = 3 + 3 y$

$- 4 x + 6 y = - 6$

Divide each term in $2 x = 3 + 3 y$ by $2$ and simplify.

Divide each term in $2 x = 3 + 3 y$ by $2$ .

$\frac{2 x}{2} = \frac{3}{2} + \frac{3 y}{2}$

$- 4 x + 6 y = - 6$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{3}{2} + \frac{3 y}{2}$

$- 4 x + 6 y = - 6$

Divide $x$ by $1$ .

$x = \frac{3}{2} + \frac{3 y}{2}$

$- 4 x + 6 y = - 6$

$x = \frac{3}{2} + \frac{3 y}{2}$

$- 4 x + 6 y = - 6$

$x = \frac{3}{2} + \frac{3 y}{2}$

$- 4 x + 6 y = - 6$

$x = \frac{3}{2} + \frac{3 y}{2}$

$- 4 x + 6 y = - 6$

$x = \frac{3}{2} + \frac{3 y}{2}$

$- 4 x + 6 y = - 6$

Step 2

Replace all occurrences of $x$ with $\frac{3}{2} + \frac{3 y}{2}$ in each equation.

Replace all occurrences of $x$ in $- 4 x + 6 y = - 6$ with $\frac{3}{2} + \frac{3 y}{2}$ .

$- 4 (\frac{3}{2} + \frac{3 y}{2}) + 6 y = - 6$

$x = \frac{3}{2} + \frac{3 y}{2}$

Simplify the left side.

Simplify $- 4 (\frac{3}{2} + \frac{3 y}{2}) + 6 y$ .

Simplify each term.

Apply the distributive property.

$- 4 (\frac{3}{2}) - 4 \frac{3 y}{2} + 6 y = - 6$

$x = \frac{3}{2} + \frac{3 y}{2}$

Cancel the common factor of $2$ .

Factor $2$ out of $- 4$ .

$2 (- 2) (\frac{3}{2}) - 4 \frac{3 y}{2} + 6 y = - 6$

$x = \frac{3}{2} + \frac{3 y}{2}$

Cancel the common factor.

$2 \cdot (- 2 (\frac{3}{2})) - 4 \frac{3 y}{2} + 6 y = - 6$

$x = \frac{3}{2} + \frac{3 y}{2}$

Rewrite the expression.

$- 2 \cdot 3 - 4 \frac{3 y}{2} + 6 y = - 6$

$x = \frac{3}{2} + \frac{3 y}{2}$

$- 2 \cdot 3 - 4 \frac{3 y}{2} + 6 y = - 6$

$x = \frac{3}{2} + \frac{3 y}{2}$

Multiply $- 2$ by $3$ .

$- 6 - 4 \frac{3 y}{2} + 6 y = - 6$

$x = \frac{3}{2} + \frac{3 y}{2}$

Cancel the common factor of $2$ .

Factor $2$ out of $- 4$ .

$- 6 + 2 (- 2) (\frac{3 y}{2}) + 6 y = - 6$

$x = \frac{3}{2} + \frac{3 y}{2}$

Cancel the common factor.

$- 6 + 2 \cdot (- 2 \frac{3 y}{2}) + 6 y = - 6$

$x = \frac{3}{2} + \frac{3 y}{2}$

Rewrite the expression.

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

$x = \frac{3}{2} + \frac{3 y}{2}$

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

$x = \frac{3}{2} + \frac{3 y}{2}$

Multiply $3$ by $- 2$ .

$- 6 - 6 y + 6 y = - 6$

$x = \frac{3}{2} + \frac{3 y}{2}$

$- 6 - 6 y + 6 y = - 6$

$x = \frac{3}{2} + \frac{3 y}{2}$

Combine the opposite terms in $- 6 - 6 y + 6 y$ .

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

$- 6 + 0 = - 6$

$x = \frac{3}{2} + \frac{3 y}{2}$

Add $- 6$ and $0$ .

$- 6 = - 6$

$x = \frac{3}{2} + \frac{3 y}{2}$

$- 6 = - 6$

$x = \frac{3}{2} + \frac{3 y}{2}$

$- 6 = - 6$

$x = \frac{3}{2} + \frac{3 y}{2}$

$- 6 = - 6$

$x = \frac{3}{2} + \frac{3 y}{2}$

$- 6 = - 6$

$x = \frac{3}{2} + \frac{3 y}{2}$

Step 3

Remove any equations from the system that are always true.

$x = \frac{3}{2} + \frac{3 y}{2}$

Step 4

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