Solve the System of Equations 5x-y=-9 and 3x+4y=13

$5 x - y = - 9$ and $3 x + 4 y = 13$

Solve for $x$ in $5 x - y = - 9$ .

Add $y$ to both sides of the equation.

$5 x = - 9 + y$

$3 x + 4 y = 13$

Divide each term in $5 x = - 9 + y$ by $5$ and simplify.

Divide each term in $5 x = - 9 + y$ by $5$ .

$\frac{5 x}{5} = \frac{- 9}{5} + \frac{y}{5}$

$3 x + 4 y = 13$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 9}{5} + \frac{y}{5}$

$3 x + 4 y = 13$

Divide $x$ by $1$ .

$x = \frac{- 9}{5} + \frac{y}{5}$

$3 x + 4 y = 13$

$x = \frac{- 9}{5} + \frac{y}{5}$

$3 x + 4 y = 13$

$x = \frac{- 9}{5} + \frac{y}{5}$

$3 x + 4 y = 13$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{9}{5} + \frac{y}{5}$

$3 x + 4 y = 13$

$x = - \frac{9}{5} + \frac{y}{5}$

$3 x + 4 y = 13$

$x = - \frac{9}{5} + \frac{y}{5}$

$3 x + 4 y = 13$

$x = - \frac{9}{5} + \frac{y}{5}$

$3 x + 4 y = 13$

Replace all occurrences of $x$ with $- \frac{9}{5} + \frac{y}{5}$ in each equation.

Replace all occurrences of $x$ in $3 x + 4 y = 13$ with $- \frac{9}{5} + \frac{y}{5}$ .

$3 (- \frac{9}{5} + \frac{y}{5}) + 4 y = 13$

$x = - \frac{9}{5} + \frac{y}{5}$

Simplify the left side.

Simplify $3 (- \frac{9}{5} + \frac{y}{5}) + 4 y$ .

Simplify each term.

Apply the distributive property.

$3 (- \frac{9}{5}) + 3 (\frac{y}{5}) + 4 y = 13$

$x = - \frac{9}{5} + \frac{y}{5}$

Multiply $3 (- \frac{9}{5})$ .

Multiply $- 1$ by $3$ .

$- 3 (\frac{9}{5}) + 3 (\frac{y}{5}) + 4 y = 13$

$x = - \frac{9}{5} + \frac{y}{5}$

Combine $- 3$ and $\frac{9}{5}$ .

$\frac{- 3 \cdot 9}{5} + 3 (\frac{y}{5}) + 4 y = 13$

$x = - \frac{9}{5} + \frac{y}{5}$

Multiply $- 3$ by $9$ .

$\frac{- 27}{5} + 3 (\frac{y}{5}) + 4 y = 13$

$x = - \frac{9}{5} + \frac{y}{5}$

$\frac{- 27}{5} + 3 (\frac{y}{5}) + 4 y = 13$

$x = - \frac{9}{5} + \frac{y}{5}$

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

$\frac{- 27}{5} + \frac{3 y}{5} + 4 y = 13$

$x = - \frac{9}{5} + \frac{y}{5}$

Move the negative in front of the fraction.

$- \frac{27}{5} + \frac{3 y}{5} + 4 y = 13$

$x = - \frac{9}{5} + \frac{y}{5}$

$- \frac{27}{5} + \frac{3 y}{5} + 4 y = 13$

$x = - \frac{9}{5} + \frac{y}{5}$

To write $4 y$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- \frac{27}{5} + \frac{3 y}{5} + 4 y \cdot \frac{5}{5} = 13$

$x = - \frac{9}{5} + \frac{y}{5}$

Combine $4 y$ and $\frac{5}{5}$ .

$- \frac{27}{5} + \frac{3 y}{5} + \frac{4 y \cdot 5}{5} = 13$

$x = - \frac{9}{5} + \frac{y}{5}$

Combine the numerators over the common denominator.

$- \frac{27}{5} + \frac{3 y + 4 y \cdot 5}{5} = 13$

$x = - \frac{9}{5} + \frac{y}{5}$

Combine the numerators over the common denominator.

$\frac{- 27 + 3 y + 4 y \cdot 5}{5} = 13$

$x = - \frac{9}{5} + \frac{y}{5}$

Multiply $5$ by $4$ .

$\frac{- 27 + 3 y + 20 y}{5} = 13$

$x = - \frac{9}{5} + \frac{y}{5}$

Add $3 y$ and $20 y$ .

$\frac{- 27 + 23 y}{5} = 13$

$x = - \frac{9}{5} + \frac{y}{5}$

Rewrite $- 27$ as $- 1 (27)$ .

$\frac{- 1 \cdot 27 + 23 y}{5} = 13$

$x = - \frac{9}{5} + \frac{y}{5}$

Factor $- 1$ out of $23 y$ .

$\frac{- 1 \cdot 27 - (- 23 y)}{5} = 13$

$x = - \frac{9}{5} + \frac{y}{5}$

Factor $- 1$ out of $- 1 (27) - (- 23 y)$ .

$\frac{- 1 (27 - 23 y)}{5} = 13$

$x = - \frac{9}{5} + \frac{y}{5}$

Move the negative in front of the fraction.

$- \frac{27 - 23 y}{5} = 13$

$x = - \frac{9}{5} + \frac{y}{5}$

$- \frac{27 - 23 y}{5} = 13$

$x = - \frac{9}{5} + \frac{y}{5}$

$- \frac{27 - 23 y}{5} = 13$

$x = - \frac{9}{5} + \frac{y}{5}$

$- \frac{27 - 23 y}{5} = 13$

$x = - \frac{9}{5} + \frac{y}{5}$

Solve for $y$ in $- \frac{27 - 23 y}{5} = 13$ .

Multiply both sides of the equation by $- 5$ .

$- 5 (- \frac{27 - 23 y}{5}) = - 5 \cdot 13$

$x = - \frac{9}{5} + \frac{y}{5}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 5 (- \frac{27 - 23 y}{5})$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{27 - 23 y}{5}$ into the numerator.

$- 5 \frac{- (27 - 23 y)}{5} = - 5 \cdot 13$

$x = - \frac{9}{5} + \frac{y}{5}$

Factor $5$ out of $- 5$ .

$5 (- 1) (\frac{- (27 - 23 y)}{5}) = - 5 \cdot 13$

$x = - \frac{9}{5} + \frac{y}{5}$

Cancel the common factor.

$5 \cdot (- 1 \frac{- (27 - 23 y)}{5}) = - 5 \cdot 13$

$x = - \frac{9}{5} + \frac{y}{5}$

Rewrite the expression.

$27 - 23 y = - 5 \cdot 13$

$x = - \frac{9}{5} + \frac{y}{5}$

$27 - 23 y = - 5 \cdot 13$

$x = - \frac{9}{5} + \frac{y}{5}$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 (27 - 23 y) = - 5 \cdot 13$

$x = - \frac{9}{5} + \frac{y}{5}$

Multiply $27 - 23 y$ by $1$ .

$27 - 23 y = - 5 \cdot 13$

$x = - \frac{9}{5} + \frac{y}{5}$

$27 - 23 y = - 5 \cdot 13$

$x = - \frac{9}{5} + \frac{y}{5}$

$27 - 23 y = - 5 \cdot 13$

$x = - \frac{9}{5} + \frac{y}{5}$

$27 - 23 y = - 5 \cdot 13$

$x = - \frac{9}{5} + \frac{y}{5}$

Simplify the right side.

Multiply $- 5$ by $13$ .

$27 - 23 y = - 65$

$x = - \frac{9}{5} + \frac{y}{5}$

$27 - 23 y = - 65$

$x = - \frac{9}{5} + \frac{y}{5}$

$27 - 23 y = - 65$

$x = - \frac{9}{5} + \frac{y}{5}$

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

Subtract $27$ from both sides of the equation.

$- 23 y = - 65 - 27$

$x = - \frac{9}{5} + \frac{y}{5}$

Subtract $27$ from $- 65$ .

$- 23 y = - 92$

$x = - \frac{9}{5} + \frac{y}{5}$

$- 23 y = - 92$

$x = - \frac{9}{5} + \frac{y}{5}$

Divide each term in $- 23 y = - 92$ by $- 23$ and simplify.

Divide each term in $- 23 y = - 92$ by $- 23$ .

$\frac{- 23 y}{- 23} = \frac{- 92}{- 23}$

$x = - \frac{9}{5} + \frac{y}{5}$

Simplify the left side.

Cancel the common factor of $- 23$ .

Cancel the common factor.

$\frac{- 23 y}{- 23} = \frac{- 92}{- 23}$

$x = - \frac{9}{5} + \frac{y}{5}$

Divide $y$ by $1$ .

$y = \frac{- 92}{- 23}$

$x = - \frac{9}{5} + \frac{y}{5}$

$y = \frac{- 92}{- 23}$

$x = - \frac{9}{5} + \frac{y}{5}$

$y = \frac{- 92}{- 23}$

$x = - \frac{9}{5} + \frac{y}{5}$

Simplify the right side.

Divide $- 92$ by $- 23$ .

$y = 4$

$x = - \frac{9}{5} + \frac{y}{5}$

$y = 4$

$x = - \frac{9}{5} + \frac{y}{5}$

$y = 4$

$x = - \frac{9}{5} + \frac{y}{5}$

$y = 4$

$x = - \frac{9}{5} + \frac{y}{5}$

Replace all occurrences of $y$ with $4$ in each equation.

Replace all occurrences of $y$ in $x = - \frac{9}{5} + \frac{y}{5}$ with $4$ .

$x = - \frac{9}{5} + \frac{4}{5}$

$y = 4$

Simplify the right side.

Simplify $- \frac{9}{5} + \frac{4}{5}$ .

Combine the numerators over the common denominator.

$x = \frac{- 9 + 4}{5}$

$y = 4$

Simplify the expression.

Add $- 9$ and $4$ .

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

$y = 4$

Divide $- 5$ by $5$ .

$x = - 1$

$y = 4$

$x = - 1$

$y = 4$

$x = - 1$

$y = 4$

$x = - 1$

$y = 4$

$x = - 1$

$y = 4$

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

$(- 1, 4)$

The result can be shown in multiple forms.

Point Form:

$(- 1, 4)$

Equation Form:

$x = - 1, y = 4$

Solve the System of Equations 5x-y=-9 and 3x+4y=13

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