Solve by Substitution 5x-6y=3 , -10x+12y=-6

$5 x - 6 y = 3$ , $- 10 x + 12 y = - 6$

Step 1

Solve for $x$ in $5 x - 6 y = 3$ .

Add $6 y$ to both sides of the equation.

$5 x = 3 + 6 y$

$- 10 x + 12 y = - 6$

Divide each term in $5 x = 3 + 6 y$ by $5$ and simplify.

Divide each term in $5 x = 3 + 6 y$ by $5$ .

$\frac{5 x}{5} = \frac{3}{5} + \frac{6 y}{5}$

$- 10 x + 12 y = - 6$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{3}{5} + \frac{6 y}{5}$

$- 10 x + 12 y = - 6$

Divide $x$ by $1$ .

$x = \frac{3}{5} + \frac{6 y}{5}$

$- 10 x + 12 y = - 6$

$x = \frac{3}{5} + \frac{6 y}{5}$

$- 10 x + 12 y = - 6$

$x = \frac{3}{5} + \frac{6 y}{5}$

$- 10 x + 12 y = - 6$

$x = \frac{3}{5} + \frac{6 y}{5}$

$- 10 x + 12 y = - 6$

$x = \frac{3}{5} + \frac{6 y}{5}$

$- 10 x + 12 y = - 6$

Step 2

Replace all occurrences of $x$ with $\frac{3}{5} + \frac{6 y}{5}$ in each equation.

Replace all occurrences of $x$ in $- 10 x + 12 y = - 6$ with $\frac{3}{5} + \frac{6 y}{5}$ .

$- 10 (\frac{3}{5} + \frac{6 y}{5}) + 12 y = - 6$

$x = \frac{3}{5} + \frac{6 y}{5}$

Simplify the left side.

Simplify $- 10 (\frac{3}{5} + \frac{6 y}{5}) + 12 y$ .

Simplify each term.

Apply the distributive property.

$- 10 (\frac{3}{5}) - 10 \frac{6 y}{5} + 12 y = - 6$

$x = \frac{3}{5} + \frac{6 y}{5}$

Cancel the common factor of $5$ .

Factor $5$ out of $- 10$ .

$5 (- 2) (\frac{3}{5}) - 10 \frac{6 y}{5} + 12 y = - 6$

$x = \frac{3}{5} + \frac{6 y}{5}$

Cancel the common factor.

$5 \cdot (- 2 (\frac{3}{5})) - 10 \frac{6 y}{5} + 12 y = - 6$

$x = \frac{3}{5} + \frac{6 y}{5}$

Rewrite the expression.

$- 2 \cdot 3 - 10 \frac{6 y}{5} + 12 y = - 6$

$x = \frac{3}{5} + \frac{6 y}{5}$

$- 2 \cdot 3 - 10 \frac{6 y}{5} + 12 y = - 6$

$x = \frac{3}{5} + \frac{6 y}{5}$

Multiply $- 2$ by $3$ .

$- 6 - 10 \frac{6 y}{5} + 12 y = - 6$

$x = \frac{3}{5} + \frac{6 y}{5}$

Cancel the common factor of $5$ .

Factor $5$ out of $- 10$ .

$- 6 + 5 (- 2) (\frac{6 y}{5}) + 12 y = - 6$

$x = \frac{3}{5} + \frac{6 y}{5}$

Cancel the common factor.

$- 6 + 5 \cdot (- 2 \frac{6 y}{5}) + 12 y = - 6$

$x = \frac{3}{5} + \frac{6 y}{5}$

Rewrite the expression.

$- 6 - 2 (6 y) + 12 y = - 6$

$x = \frac{3}{5} + \frac{6 y}{5}$

$- 6 - 2 (6 y) + 12 y = - 6$

$x = \frac{3}{5} + \frac{6 y}{5}$

Multiply $6$ by $- 2$ .

$- 6 - 12 y + 12 y = - 6$

$x = \frac{3}{5} + \frac{6 y}{5}$

$- 6 - 12 y + 12 y = - 6$

$x = \frac{3}{5} + \frac{6 y}{5}$

Combine the opposite terms in $- 6 - 12 y + 12 y$ .

Add $- 12 y$ and $12 y$ .

$- 6 + 0 = - 6$

$x = \frac{3}{5} + \frac{6 y}{5}$

Add $- 6$ and $0$ .

$- 6 = - 6$

$x = \frac{3}{5} + \frac{6 y}{5}$

$- 6 = - 6$

$x = \frac{3}{5} + \frac{6 y}{5}$

$- 6 = - 6$

$x = \frac{3}{5} + \frac{6 y}{5}$

$- 6 = - 6$

$x = \frac{3}{5} + \frac{6 y}{5}$

$- 6 = - 6$

$x = \frac{3}{5} + \frac{6 y}{5}$

Step 3

Remove any equations from the system that are always true.

$x = \frac{3}{5} + \frac{6 y}{5}$

Step 4

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