Solve the System of Equations -5x+13y=-7 5x+4y=24

$- 5 x + 13 y = - 7$ $5 x + 4 y = 24$

Step 1

Solve for $x$ in $- 5 x + 13 y = - 7$ .

Subtract $13 y$ from both sides of the equation.

$- 5 x = - 7 - 13 y$

$5 x + 4 y = 24$

Divide each term in $- 5 x = - 7 - 13 y$ by $- 5$ and simplify.

Divide each term in $- 5 x = - 7 - 13 y$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 7}{- 5} + \frac{- 13 y}{- 5}$

$5 x + 4 y = 24$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 7}{- 5} + \frac{- 13 y}{- 5}$

$5 x + 4 y = 24$

Divide $x$ by $1$ .

$x = \frac{- 7}{- 5} + \frac{- 13 y}{- 5}$

$5 x + 4 y = 24$

$x = \frac{- 7}{- 5} + \frac{- 13 y}{- 5}$

$5 x + 4 y = 24$

$x = \frac{- 7}{- 5} + \frac{- 13 y}{- 5}$

$5 x + 4 y = 24$

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

$x = \frac{7}{5} + \frac{- 13 y}{- 5}$

$5 x + 4 y = 24$

Dividing two negative values results in a positive value.

$x = \frac{7}{5} + \frac{13 y}{5}$

$5 x + 4 y = 24$

$x = \frac{7}{5} + \frac{13 y}{5}$

$5 x + 4 y = 24$

$x = \frac{7}{5} + \frac{13 y}{5}$

$5 x + 4 y = 24$

$x = \frac{7}{5} + \frac{13 y}{5}$

$5 x + 4 y = 24$

$x = \frac{7}{5} + \frac{13 y}{5}$

$5 x + 4 y = 24$

Step 2

Replace all occurrences of $x$ with $\frac{7}{5} + \frac{13 y}{5}$ in each equation.

Replace all occurrences of $x$ in $5 x + 4 y = 24$ with $\frac{7}{5} + \frac{13 y}{5}$ .

$5 (\frac{7}{5} + \frac{13 y}{5}) + 4 y = 24$

$x = \frac{7}{5} + \frac{13 y}{5}$

Simplify the left side.

Simplify $5 (\frac{7}{5} + \frac{13 y}{5}) + 4 y$ .

Simplify each term.

Apply the distributive property.

$5 (\frac{7}{5}) + 5 (\frac{13 y}{5}) + 4 y = 24$

$x = \frac{7}{5} + \frac{13 y}{5}$

Cancel the common factor of $5$ .

Cancel the common factor.

$5 (\frac{7}{5}) + 5 (\frac{13 y}{5}) + 4 y = 24$

$x = \frac{7}{5} + \frac{13 y}{5}$

Rewrite the expression.

$7 + 5 (\frac{13 y}{5}) + 4 y = 24$

$x = \frac{7}{5} + \frac{13 y}{5}$

$7 + 5 (\frac{13 y}{5}) + 4 y = 24$

$x = \frac{7}{5} + \frac{13 y}{5}$

Cancel the common factor of $5$ .

Cancel the common factor.

$7 + 5 (\frac{13 y}{5}) + 4 y = 24$

$x = \frac{7}{5} + \frac{13 y}{5}$

Rewrite the expression.

$7 + 13 y + 4 y = 24$

$x = \frac{7}{5} + \frac{13 y}{5}$

$7 + 13 y + 4 y = 24$

$x = \frac{7}{5} + \frac{13 y}{5}$

$7 + 13 y + 4 y = 24$

$x = \frac{7}{5} + \frac{13 y}{5}$

Add $13 y$ and $4 y$ .

$7 + 17 y = 24$

$x = \frac{7}{5} + \frac{13 y}{5}$

$7 + 17 y = 24$

$x = \frac{7}{5} + \frac{13 y}{5}$

$7 + 17 y = 24$

$x = \frac{7}{5} + \frac{13 y}{5}$

$7 + 17 y = 24$

$x = \frac{7}{5} + \frac{13 y}{5}$

Step 3

Solve for $y$ in $7 + 17 y = 24$ .

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

Subtract $7$ from both sides of the equation.

$17 y = 24 - 7$

$x = \frac{7}{5} + \frac{13 y}{5}$

Subtract $7$ from $24$ .

$17 y = 17$

$x = \frac{7}{5} + \frac{13 y}{5}$

$17 y = 17$

$x = \frac{7}{5} + \frac{13 y}{5}$

Divide each term in $17 y = 17$ by $17$ and simplify.

Divide each term in $17 y = 17$ by $17$ .

$\frac{17 y}{17} = \frac{17}{17}$

$x = \frac{7}{5} + \frac{13 y}{5}$

Simplify the left side.

Cancel the common factor of $17$ .

Cancel the common factor.

$\frac{17 y}{17} = \frac{17}{17}$

$x = \frac{7}{5} + \frac{13 y}{5}$

Divide $y$ by $1$ .

$y = \frac{17}{17}$

$x = \frac{7}{5} + \frac{13 y}{5}$

$y = \frac{17}{17}$

$x = \frac{7}{5} + \frac{13 y}{5}$

$y = \frac{17}{17}$

$x = \frac{7}{5} + \frac{13 y}{5}$

Simplify the right side.

Divide $17$ by $17$ .

$y = 1$

$x = \frac{7}{5} + \frac{13 y}{5}$

$y = 1$

$x = \frac{7}{5} + \frac{13 y}{5}$

$y = 1$

$x = \frac{7}{5} + \frac{13 y}{5}$

$y = 1$

$x = \frac{7}{5} + \frac{13 y}{5}$

Step 4

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

Replace all occurrences of $y$ in $x = \frac{7}{5} + \frac{13 y}{5}$ with $1$ .

$x = \frac{7}{5} + \frac{13 (1)}{5}$

$y = 1$

Simplify the right side.

Simplify $\frac{7}{5} + \frac{13 (1)}{5}$ .

Combine the numerators over the common denominator.

$x = \frac{7 + 13 (1)}{5}$

$y = 1$

Simplify the expression.

Multiply $13$ by $1$ .

$x = \frac{7 + 13}{5}$

$y = 1$

Add $7$ and $13$ .

$x = \frac{20}{5}$

$y = 1$

Divide $20$ by $5$ .

$x = 4$

$y = 1$

$x = 4$

$y = 1$

$x = 4$

$y = 1$

$x = 4$

$y = 1$

$x = 4$

$y = 1$

Step 5

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

$(4, 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(4, 1)$

Equation Form:

$x = 4, y = 1$

Step 7

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