Solve by Substitution 5x-3y=-3 , 2x-6y=-6

$5 x - 3 y = - 3$ , $2 x - 6 y = - 6$

Step 1

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

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

$5 x = - 3 + 3 y$

$2 x - 6 y = - 6$

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

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

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

$2 x - 6 y = - 6$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

$2 x - 6 y = - 6$

Divide $x$ by $1$ .

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

$2 x - 6 y = - 6$

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

$2 x - 6 y = - 6$

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

$2 x - 6 y = - 6$

Simplify the right side.

Move the negative in front of the fraction.

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

$2 x - 6 y = - 6$

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

$2 x - 6 y = - 6$

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

$2 x - 6 y = - 6$

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

$2 x - 6 y = - 6$

Step 2

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

Replace all occurrences of $x$ in $2 x - 6 y = - 6$ with $- \frac{3}{5} + \frac{3 y}{5}$ .

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

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

Simplify the left side.

Simplify $2 (- \frac{3}{5} + \frac{3 y}{5}) - 6 y$ .

Simplify each term.

Apply the distributive property.

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

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

Multiply $2 (- \frac{3}{5})$ .

Multiply $- 1$ by $2$ .

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

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

Combine $- 2$ and $\frac{3}{5}$ .

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

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

Multiply $- 2$ by $3$ .

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

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

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

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

Multiply $2 \frac{3 y}{5}$ .

Combine $2$ and $\frac{3 y}{5}$ .

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

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

Multiply $3$ by $2$ .

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

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

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

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

Move the negative in front of the fraction.

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

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

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

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

To write $- 6 y$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{6}{5} + \frac{6 y}{5} - 6 y \cdot \frac{5}{5} = - 6$

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

Combine $- 6 y$ and $\frac{5}{5}$ .

$- \frac{6}{5} + \frac{6 y}{5} + \frac{- 6 y \cdot 5}{5} = - 6$

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

Combine the numerators over the common denominator.

$- \frac{6}{5} + \frac{6 y - 6 y \cdot 5}{5} = - 6$

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

Combine the numerators over the common denominator.

$\frac{- 6 + 6 y - 6 y \cdot 5}{5} = - 6$

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

Multiply $5$ by $- 6$ .

$\frac{- 6 + 6 y - 30 y}{5} = - 6$

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

Subtract $30 y$ from $6 y$ .

$\frac{- 6 - 24 y}{5} = - 6$

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

Factor $6$ out of $- 6 - 24 y$ .

Factor $6$ out of $- 6$ .

$\frac{6 (- 1) - 24 y}{5} = - 6$

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

Factor $6$ out of $- 24 y$ .

$\frac{6 (- 1) + 6 (- 4 y)}{5} = - 6$

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

Factor $6$ out of $6 (- 1) + 6 (- 4 y)$ .

$\frac{6 (- 1 - 4 y)}{5} = - 6$

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

$\frac{6 (- 1 - 4 y)}{5} = - 6$

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

Rewrite $- 1$ as $- 1 (1)$ .

$\frac{6 (- 1 \cdot 1 - 4 y)}{5} = - 6$

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

Factor $- 1$ out of $- 4 y$ .

$\frac{6 (- 1 \cdot 1 - (4 y))}{5} = - 6$

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

Factor $- 1$ out of $- 1 (1) - (4 y)$ .

$\frac{6 (- 1 (1 + 4 y))}{5} = - 6$

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

Move the negative in front of the fraction.

$- \frac{6 (1 + 4 y)}{5} = - 6$

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

$- \frac{6 (1 + 4 y)}{5} = - 6$

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

$- \frac{6 (1 + 4 y)}{5} = - 6$

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

$- \frac{6 (1 + 4 y)}{5} = - 6$

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

Step 3

Solve for $y$ in $- \frac{6 (1 + 4 y)}{5} = - 6$ .

Multiply both sides of the equation by $- \frac{5}{6}$ .

$- \frac{5}{6} \cdot (- \frac{6 (1 + 4 y)}{5}) = - \frac{5}{6} \cdot - 6$

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

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{5}{6} (- \frac{6 (1 + 4 y)}{5})$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{5}{6}$ into the numerator.

$\frac{- 5}{6} \cdot (- \frac{6 (1 + 4 y)}{5}) = - \frac{5}{6} \cdot - 6$

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

Move the leading negative in $- \frac{6 (1 + 4 y)}{5}$ into the numerator.

$\frac{- 5}{6} \cdot \frac{- 6 (1 + 4 y)}{5} = - \frac{5}{6} \cdot - 6$

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

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{6} \cdot \frac{- 6 (1 + 4 y)}{5} = - \frac{5}{6} \cdot - 6$

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

Cancel the common factor.

$\frac{5 \cdot - 1}{6} \cdot \frac{- 6 (1 + 4 y)}{5} = - \frac{5}{6} \cdot - 6$

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

Rewrite the expression.

$\frac{- 1}{6} \cdot (- 6 (1 + 4 y)) = - \frac{5}{6} \cdot - 6$

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

$\frac{- 1}{6} \cdot (- 6 (1 + 4 y)) = - \frac{5}{6} \cdot - 6$

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

Cancel the common factor of $6$ .

Factor $6$ out of $- 6 (1 + 4 y)$ .

$\frac{- 1}{6} \cdot (6 (- (1 + 4 y))) = - \frac{5}{6} \cdot - 6$

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

Cancel the common factor.

$\frac{- 1}{6} \cdot (6 (- (1 + 4 y))) = - \frac{5}{6} \cdot - 6$

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

Rewrite the expression.

$1 + 4 y = - \frac{5}{6} \cdot - 6$

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

$1 + 4 y = - \frac{5}{6} \cdot - 6$

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

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (1 + 4 y) = - \frac{5}{6} \cdot - 6$

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

Multiply $1 + 4 y$ by $1$ .

$1 + 4 y = - \frac{5}{6} \cdot - 6$

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

$1 + 4 y = - \frac{5}{6} \cdot - 6$

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

$1 + 4 y = - \frac{5}{6} \cdot - 6$

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

$1 + 4 y = - \frac{5}{6} \cdot - 6$

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

Simplify the right side.

Simplify $- \frac{5}{6} \cdot - 6$ .

Cancel the common factor of $6$ .

Move the leading negative in $- \frac{5}{6}$ into the numerator.

$1 + 4 y = \frac{- 5}{6} \cdot - 6$

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

Factor $6$ out of $- 6$ .

$1 + 4 y = \frac{- 5}{6} \cdot (6 (- 1))$

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

Cancel the common factor.

$1 + 4 y = \frac{- 5}{6} \cdot (6 \cdot - 1)$

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

Rewrite the expression.

$1 + 4 y = - 5 \cdot - 1$

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

$1 + 4 y = - 5 \cdot - 1$

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

Multiply $- 5$ by $- 1$ .

$1 + 4 y = 5$

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

$1 + 4 y = 5$

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

$1 + 4 y = 5$

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

$1 + 4 y = 5$

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

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

Subtract $1$ from both sides of the equation.

$4 y = 5 - 1$

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

Subtract $1$ from $5$ .

$4 y = 4$

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

$4 y = 4$

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

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

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

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

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

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

Divide $y$ by $1$ .

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

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

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

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

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

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

Simplify the right side.

Divide $4$ by $4$ .

$y = 1$

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

$y = 1$

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

$y = 1$

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

$y = 1$

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

Step 4

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

Replace all occurrences of $y$ in $x = - \frac{3}{5} + \frac{3 y}{5}$ with $1$ .

$x = - \frac{3}{5} + \frac{3 (1)}{5}$

$y = 1$

Simplify the right side.

Simplify $- \frac{3}{5} + \frac{3 (1)}{5}$ .

Combine the numerators over the common denominator.

$x = \frac{- 3 + 3 (1)}{5}$

$y = 1$

Simplify the expression.

Multiply $3$ by $1$ .

$x = \frac{- 3 + 3}{5}$

$y = 1$

Add $- 3$ and $3$ .

$x = \frac{0}{5}$

$y = 1$

Divide $0$ by $5$ .

$x = 0$

$y = 1$

$x = 0$

$y = 1$

$x = 0$

$y = 1$

$x = 0$

$y = 1$

$x = 0$

$y = 1$

Step 5

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

$(0, 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(0, 1)$

Equation Form:

$x = 0, y = 1$

Step 7

Solve by Substitution 5x-3y=-3 , 2x-6y=-6

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