Solve the System of Equations -x-5y=18 and -x+4y=-18

$- x - 5 y = 18$ and $- x + 4 y = - 18$

Step 1

Solve for $x$ in $- x - 5 y = 18$ .

Add $5 y$ to both sides of the equation.

$- x = 18 + 5 y$

$- x + 4 y = - 18$

Divide each term in $- x = 18 + 5 y$ by $- 1$ and simplify.

Divide each term in $- x = 18 + 5 y$ by $- 1$ .

$\frac{- x}{- 1} = \frac{18}{- 1} + \frac{5 y}{- 1}$

$- x + 4 y = - 18$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{18}{- 1} + \frac{5 y}{- 1}$

$- x + 4 y = - 18$

Divide $x$ by $1$ .

$x = \frac{18}{- 1} + \frac{5 y}{- 1}$

$- x + 4 y = - 18$

$x = \frac{18}{- 1} + \frac{5 y}{- 1}$

$- x + 4 y = - 18$

Simplify the right side.

Simplify each term.

Divide $18$ by $- 1$ .

$x = - 18 + \frac{5 y}{- 1}$

$- x + 4 y = - 18$

Move the negative one from the denominator of $\frac{5 y}{- 1}$ .

$x = - 18 - 1 \cdot (5 y)$

$- x + 4 y = - 18$

Rewrite $- 1 \cdot (5 y)$ as $- (5 y)$ .

$x = - 18 - (5 y)$

$- x + 4 y = - 18$

Multiply $5$ by $- 1$ .

$x = - 18 - 5 y$

$- x + 4 y = - 18$

$x = - 18 - 5 y$

$- x + 4 y = - 18$

$x = - 18 - 5 y$

$- x + 4 y = - 18$

$x = - 18 - 5 y$

$- x + 4 y = - 18$

$x = - 18 - 5 y$

$- x + 4 y = - 18$

Step 2

Replace all occurrences of $x$ with $- 18 - 5 y$ in each equation.

Replace all occurrences of $x$ in $- x + 4 y = - 18$ with $- 18 - 5 y$ .

$- (- 18 - 5 y) + 4 y = - 18$

$x = - 18 - 5 y$

Simplify the left side.

Simplify $- (- 18 - 5 y) + 4 y$ .

Simplify each term.

Apply the distributive property.

$18 - (- 5 y) + 4 y = - 18$

$x = - 18 - 5 y$

Multiply $- 1$ by $- 18$ .

$18 - (- 5 y) + 4 y = - 18$

$x = - 18 - 5 y$

Multiply $- 5$ by $- 1$ .

$18 + 5 y + 4 y = - 18$

$x = - 18 - 5 y$

$18 + 5 y + 4 y = - 18$

$x = - 18 - 5 y$

Add $5 y$ and $4 y$ .

$18 + 9 y = - 18$

$x = - 18 - 5 y$

$18 + 9 y = - 18$

$x = - 18 - 5 y$

$18 + 9 y = - 18$

$x = - 18 - 5 y$

$18 + 9 y = - 18$

$x = - 18 - 5 y$

Step 3

Solve for $y$ in $18 + 9 y = - 18$ .

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

Subtract $18$ from both sides of the equation.

$9 y = - 18 - 18$

$x = - 18 - 5 y$

Subtract $18$ from $- 18$ .

$9 y = - 36$

$x = - 18 - 5 y$

$9 y = - 36$

$x = - 18 - 5 y$

Divide each term in $9 y = - 36$ by $9$ and simplify.

Divide each term in $9 y = - 36$ by $9$ .

$\frac{9 y}{9} = \frac{- 36}{9}$

$x = - 18 - 5 y$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 y}{9} = \frac{- 36}{9}$

$x = - 18 - 5 y$

Divide $y$ by $1$ .

$y = \frac{- 36}{9}$

$x = - 18 - 5 y$

$y = \frac{- 36}{9}$

$x = - 18 - 5 y$

$y = \frac{- 36}{9}$

$x = - 18 - 5 y$

Simplify the right side.

Divide $- 36$ by $9$ .

$y = - 4$

$x = - 18 - 5 y$

$y = - 4$

$x = - 18 - 5 y$

$y = - 4$

$x = - 18 - 5 y$

$y = - 4$

$x = - 18 - 5 y$

Step 4

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

Replace all occurrences of $y$ in $x = - 18 - 5 y$ with $- 4$ .

$x = - 18 - 5 \cdot - 4$

$y = - 4$

Simplify the right side.

Simplify $- 18 - 5 \cdot - 4$ .

Multiply $- 5$ by $- 4$ .

$x = - 18 + 20$

$y = - 4$

Add $- 18$ and $20$ .

$x = 2$

$y = - 4$

$x = 2$

$y = - 4$

$x = 2$

$y = - 4$

$x = 2$

$y = - 4$

Step 5

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

$(2, - 4)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(2, - 4)$

Equation Form:

$x = 2, y = - 4$

Step 7

Solve the System of Equations -x-5y=18 and -x+4y=-18

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