Solve by Substitution 5x-y=-5 and 3x-6y=24

$5 x - y = - 5$ and $3 x - 6 y = 24$

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

Add $y$ to both sides of the equation.

$5 x = - 5 + y$

$3 x - 6 y = 24$

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

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

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

$3 x - 6 y = 24$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

$3 x - 6 y = 24$

Divide $x$ by $1$ .

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

$3 x - 6 y = 24$

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

$3 x - 6 y = 24$

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

$3 x - 6 y = 24$

Simplify the right side.

Divide $- 5$ by $5$ .

$x = - 1 + \frac{y}{5}$

$3 x - 6 y = 24$

$x = - 1 + \frac{y}{5}$

$3 x - 6 y = 24$

$x = - 1 + \frac{y}{5}$

$3 x - 6 y = 24$

$x = - 1 + \frac{y}{5}$

$3 x - 6 y = 24$

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

Replace all occurrences of $x$ in $3 x - 6 y = 24$ with $- 1 + \frac{y}{5}$ .

$3 (- 1 + \frac{y}{5}) - 6 y = 24$

$x = - 1 + \frac{y}{5}$

Simplify the left side.

Simplify $3 (- 1 + \frac{y}{5}) - 6 y$ .

Simplify each term.

Apply the distributive property.

$3 \cdot - 1 + 3 (\frac{y}{5}) - 6 y = 24$

$x = - 1 + \frac{y}{5}$

Multiply $3$ by $- 1$ .

$- 3 + 3 (\frac{y}{5}) - 6 y = 24$

$x = - 1 + \frac{y}{5}$

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

$- 3 + \frac{3 y}{5} - 6 y = 24$

$x = - 1 + \frac{y}{5}$

$- 3 + \frac{3 y}{5} - 6 y = 24$

$x = - 1 + \frac{y}{5}$

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

$- 3 + \frac{3 y}{5} - 6 y \cdot \frac{5}{5} = 24$

$x = - 1 + \frac{y}{5}$

Simplify terms.

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

$- 3 + \frac{3 y}{5} + \frac{- 6 y \cdot 5}{5} = 24$

$x = - 1 + \frac{y}{5}$

Combine the numerators over the common denominator.

$- 3 + \frac{3 y - 6 y \cdot 5}{5} = 24$

$x = - 1 + \frac{y}{5}$

$- 3 + \frac{3 y - 6 y \cdot 5}{5} = 24$

$x = - 1 + \frac{y}{5}$

Simplify each term.

Simplify the numerator.

Factor $3 y$ out of $3 y - 6 y \cdot 5$ .

Factor $3 y$ out of $3 y$ .

$- 3 + \frac{3 y (1) - 6 y \cdot 5}{5} = 24$

$x = - 1 + \frac{y}{5}$

Factor $3 y$ out of $- 6 y \cdot 5$ .

$- 3 + \frac{3 y (1) + 3 y (- 2 \cdot 5)}{5} = 24$

$x = - 1 + \frac{y}{5}$

Factor $3 y$ out of $3 y (1) + 3 y (- 2 \cdot 5)$ .

$- 3 + \frac{3 y (1 - 2 \cdot 5)}{5} = 24$

$x = - 1 + \frac{y}{5}$

$- 3 + \frac{3 y (1 - 2 \cdot 5)}{5} = 24$

$x = - 1 + \frac{y}{5}$

Multiply $- 2$ by $5$ .

$- 3 + \frac{3 y (1 - 10)}{5} = 24$

$x = - 1 + \frac{y}{5}$

Subtract $10$ from $1$ .

$- 3 + \frac{3 y \cdot - 9}{5} = 24$

$x = - 1 + \frac{y}{5}$

Multiply $- 9$ by $3$ .

$- 3 + \frac{- 27 y}{5} = 24$

$x = - 1 + \frac{y}{5}$

$- 3 + \frac{- 27 y}{5} = 24$

$x = - 1 + \frac{y}{5}$

Move the negative in front of the fraction.

$- 3 - \frac{27 y}{5} = 24$

$x = - 1 + \frac{y}{5}$

$- 3 - \frac{27 y}{5} = 24$

$x = - 1 + \frac{y}{5}$

$- 3 - \frac{27 y}{5} = 24$

$x = - 1 + \frac{y}{5}$

$- 3 - \frac{27 y}{5} = 24$

$x = - 1 + \frac{y}{5}$

$- 3 - \frac{27 y}{5} = 24$

$x = - 1 + \frac{y}{5}$

Solve for $y$ in $- 3 - \frac{27 y}{5} = 24$ .

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

Add $3$ to both sides of the equation.

$- \frac{27 y}{5} = 24 + 3$

$x = - 1 + \frac{y}{5}$

Add $24$ and $3$ .

$- \frac{27 y}{5} = 27$

$x = - 1 + \frac{y}{5}$

$- \frac{27 y}{5} = 27$

$x = - 1 + \frac{y}{5}$

Multiply both sides of the equation by $- \frac{5}{27}$ .

$- \frac{5}{27} \cdot (- \frac{27 y}{5}) = - \frac{5}{27} \cdot 27$

$x = - 1 + \frac{y}{5}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{5}{27} (- \frac{27 y}{5})$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{5}{27}$ into the numerator.

$\frac{- 5}{27} \cdot (- \frac{27 y}{5}) = - \frac{5}{27} \cdot 27$

$x = - 1 + \frac{y}{5}$

Move the leading negative in $- \frac{27 y}{5}$ into the numerator.

$\frac{- 5}{27} \cdot \frac{- 27 y}{5} = - \frac{5}{27} \cdot 27$

$x = - 1 + \frac{y}{5}$

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{27} \cdot \frac{- 27 y}{5} = - \frac{5}{27} \cdot 27$

$x = - 1 + \frac{y}{5}$

Cancel the common factor.

$\frac{5 \cdot - 1}{27} \cdot \frac{- 27 y}{5} = - \frac{5}{27} \cdot 27$

$x = - 1 + \frac{y}{5}$

Rewrite the expression.

$\frac{- 1}{27} \cdot (- 27 y) = - \frac{5}{27} \cdot 27$

$x = - 1 + \frac{y}{5}$

$\frac{- 1}{27} \cdot (- 27 y) = - \frac{5}{27} \cdot 27$

$x = - 1 + \frac{y}{5}$

Cancel the common factor of $27$ .

Factor $27$ out of $- 27 y$ .

$\frac{- 1}{27} \cdot (27 (- y)) = - \frac{5}{27} \cdot 27$

$x = - 1 + \frac{y}{5}$

Cancel the common factor.

$\frac{- 1}{27} \cdot (27 (- y)) = - \frac{5}{27} \cdot 27$

$x = - 1 + \frac{y}{5}$

Rewrite the expression.

$y = - \frac{5}{27} \cdot 27$

$x = - 1 + \frac{y}{5}$

$y = - \frac{5}{27} \cdot 27$

$x = - 1 + \frac{y}{5}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{5}{27} \cdot 27$

$x = - 1 + \frac{y}{5}$

Multiply $y$ by $1$ .

$y = - \frac{5}{27} \cdot 27$

$x = - 1 + \frac{y}{5}$

$y = - \frac{5}{27} \cdot 27$

$x = - 1 + \frac{y}{5}$

$y = - \frac{5}{27} \cdot 27$

$x = - 1 + \frac{y}{5}$

$y = - \frac{5}{27} \cdot 27$

$x = - 1 + \frac{y}{5}$

Simplify the right side.

Cancel the common factor of $27$ .

Move the leading negative in $- \frac{5}{27}$ into the numerator.

$y = \frac{- 5}{27} \cdot 27$

$x = - 1 + \frac{y}{5}$

Cancel the common factor.

$y = \frac{- 5}{27} \cdot 27$

$x = - 1 + \frac{y}{5}$

Rewrite the expression.

$y = - 5$

$x = - 1 + \frac{y}{5}$

$y = - 5$

$x = - 1 + \frac{y}{5}$

$y = - 5$

$x = - 1 + \frac{y}{5}$

$y = - 5$

$x = - 1 + \frac{y}{5}$

$y = - 5$

$x = - 1 + \frac{y}{5}$

Replace all occurrences of $y$ with $- 5$ in each equation.

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

$x = - 1 + \frac{- 5}{5}$

$y = - 5$

Simplify the right side.

Simplify $- 1 + \frac{- 5}{5}$ .

Divide $- 5$ by $5$ .

$x = - 1 - 1$

$y = - 5$

Subtract $1$ from $- 1$ .

$x = - 2$

$y = - 5$

$x = - 2$

$y = - 5$

$x = - 2$

$y = - 5$

$x = - 2$

$y = - 5$

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

$(- 2, - 5)$

The result can be shown in multiple forms.

Point Form:

$(- 2, - 5)$

Equation Form:

$x = - 2, y = - 5$

Solve by Substitution 5x-y=-5 and 3x-6y=24

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