Solve the System of Equations -4y-11x=36 20=-10x-10y

$- 4 y - 11 x = 36$ $20 = - 10 x - 10 y$

Step 1

Solve for $y$ in $- 4 y - 11 x = 36$ .

Add $11 x$ to both sides of the equation.

$- 4 y = 36 + 11 x$

$20 = - 10 x - 10 y$

Divide each term in $- 4 y = 36 + 11 x$ by $- 4$ and simplify.

Divide each term in $- 4 y = 36 + 11 x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{36}{- 4} + \frac{11 x}{- 4}$

$20 = - 10 x - 10 y$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{36}{- 4} + \frac{11 x}{- 4}$

$20 = - 10 x - 10 y$

Divide $y$ by $1$ .

$y = \frac{36}{- 4} + \frac{11 x}{- 4}$

$20 = - 10 x - 10 y$

$y = \frac{36}{- 4} + \frac{11 x}{- 4}$

$20 = - 10 x - 10 y$

$y = \frac{36}{- 4} + \frac{11 x}{- 4}$

$20 = - 10 x - 10 y$

Simplify the right side.

Simplify each term.

Divide $36$ by $- 4$ .

$y = - 9 + \frac{11 x}{- 4}$

$20 = - 10 x - 10 y$

Move the negative in front of the fraction.

$y = - 9 - \frac{11 x}{4}$

$20 = - 10 x - 10 y$

$y = - 9 - \frac{11 x}{4}$

$20 = - 10 x - 10 y$

$y = - 9 - \frac{11 x}{4}$

$20 = - 10 x - 10 y$

$y = - 9 - \frac{11 x}{4}$

$20 = - 10 x - 10 y$

$y = - 9 - \frac{11 x}{4}$

$20 = - 10 x - 10 y$

Step 2

Replace all occurrences of $y$ with $- 9 - \frac{11 x}{4}$ in each equation.

Replace all occurrences of $y$ in $20 = - 10 x - 10 y$ with $- 9 - \frac{11 x}{4}$ .

$20 = - 10 x - 10 (- 9 - \frac{11 x}{4})$

$y = - 9 - \frac{11 x}{4}$

Simplify the right side.

Simplify $- 10 x - 10 (- 9 - \frac{11 x}{4})$ .

Simplify each term.

Apply the distributive property.

$20 = - 10 x - 10 \cdot - 9 - 10 (- \frac{11 x}{4})$

$y = - 9 - \frac{11 x}{4}$

Multiply $- 10$ by $- 9$ .

$20 = - 10 x + 90 - 10 (- \frac{11 x}{4})$

$y = - 9 - \frac{11 x}{4}$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{11 x}{4}$ into the numerator.

$20 = - 10 x + 90 - 10 \frac{- 11 x}{4}$

$y = - 9 - \frac{11 x}{4}$

Factor $2$ out of $- 10$ .

$20 = - 10 x + 90 + 2 (- 5) (\frac{- 11 x}{4})$

$y = - 9 - \frac{11 x}{4}$

Factor $2$ out of $4$ .

$20 = - 10 x + 90 + 2 \cdot (- 5 \frac{- 11 x}{2 \cdot 2})$

$y = - 9 - \frac{11 x}{4}$

Cancel the common factor.

$20 = - 10 x + 90 + 2 \cdot (- 5 \frac{- 11 x}{2 \cdot 2})$

$y = - 9 - \frac{11 x}{4}$

Rewrite the expression.

$20 = - 10 x + 90 - 5 \frac{- 11 x}{2}$

$y = - 9 - \frac{11 x}{4}$

$20 = - 10 x + 90 - 5 \frac{- 11 x}{2}$

$y = - 9 - \frac{11 x}{4}$

Combine $- 5$ and $\frac{- 11 x}{2}$ .

$20 = - 10 x + 90 + \frac{- 5 (- 11 x)}{2}$

$y = - 9 - \frac{11 x}{4}$

Multiply $- 11$ by $- 5$ .

$20 = - 10 x + 90 + \frac{55 x}{2}$

$y = - 9 - \frac{11 x}{4}$

$20 = - 10 x + 90 + \frac{55 x}{2}$

$y = - 9 - \frac{11 x}{4}$

To write $- 10 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$20 = - 10 x \cdot \frac{2}{2} + \frac{55 x}{2} + 90$

$y = - 9 - \frac{11 x}{4}$

Simplify terms.

Combine $- 10 x$ and $\frac{2}{2}$ .

$20 = \frac{- 10 x \cdot 2}{2} + \frac{55 x}{2} + 90$

$y = - 9 - \frac{11 x}{4}$

Combine the numerators over the common denominator.

$20 = \frac{- 10 x \cdot 2 + 55 x}{2} + 90$

$y = - 9 - \frac{11 x}{4}$

$20 = \frac{- 10 x \cdot 2 + 55 x}{2} + 90$

$y = - 9 - \frac{11 x}{4}$

Simplify the numerator.

Factor $5 x$ out of $- 10 x \cdot 2 + 55 x$ .

Factor $5 x$ out of $- 10 x \cdot 2$ .

$20 = \frac{5 x (- 2 \cdot 2) + 55 x}{2} + 90$

$y = - 9 - \frac{11 x}{4}$

Factor $5 x$ out of $55 x$ .

$20 = \frac{5 x (- 2 \cdot 2) + 5 x (11)}{2} + 90$

$y = - 9 - \frac{11 x}{4}$

Factor $5 x$ out of $5 x (- 2 \cdot 2) + 5 x (11)$ .

$20 = \frac{5 x (- 2 \cdot 2 + 11)}{2} + 90$

$y = - 9 - \frac{11 x}{4}$

$20 = \frac{5 x (- 2 \cdot 2 + 11)}{2} + 90$

$y = - 9 - \frac{11 x}{4}$

Multiply $- 2$ by $2$ .

$20 = \frac{5 x (- 4 + 11)}{2} + 90$

$y = - 9 - \frac{11 x}{4}$

Add $- 4$ and $11$ .

$20 = \frac{5 x \cdot 7}{2} + 90$

$y = - 9 - \frac{11 x}{4}$

Multiply $7$ by $5$ .

$20 = \frac{35 x}{2} + 90$

$y = - 9 - \frac{11 x}{4}$

$20 = \frac{35 x}{2} + 90$

$y = - 9 - \frac{11 x}{4}$

$20 = \frac{35 x}{2} + 90$

$y = - 9 - \frac{11 x}{4}$

$20 = \frac{35 x}{2} + 90$

$y = - 9 - \frac{11 x}{4}$

$20 = \frac{35 x}{2} + 90$

$y = - 9 - \frac{11 x}{4}$

Step 3

Solve for $x$ in $20 = \frac{35 x}{2} + 90$ .

Rewrite the equation as $\frac{35 x}{2} + 90 = 20$ .

$\frac{35 x}{2} + 90 = 20$

$y = - 9 - \frac{11 x}{4}$

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

Subtract $90$ from both sides of the equation.

$\frac{35 x}{2} = 20 - 90$

$y = - 9 - \frac{11 x}{4}$

Subtract $90$ from $20$ .

$\frac{35 x}{2} = - 70$

$y = - 9 - \frac{11 x}{4}$

$\frac{35 x}{2} = - 70$

$y = - 9 - \frac{11 x}{4}$

Multiply both sides of the equation by $\frac{2}{35}$ .

$\frac{2}{35} \cdot \frac{35 x}{2} = \frac{2}{35} \cdot - 70$

$y = - 9 - \frac{11 x}{4}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{2}{35} \cdot \frac{35 x}{2}$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2}{35} \cdot \frac{35 x}{2} = \frac{2}{35} \cdot - 70$

$y = - 9 - \frac{11 x}{4}$

Rewrite the expression.

$\frac{1}{35} \cdot (35 x) = \frac{2}{35} \cdot - 70$

$y = - 9 - \frac{11 x}{4}$

$\frac{1}{35} \cdot (35 x) = \frac{2}{35} \cdot - 70$

$y = - 9 - \frac{11 x}{4}$

Cancel the common factor of $35$ .

Factor $35$ out of $35 x$ .

$\frac{1}{35} \cdot (35 (x)) = \frac{2}{35} \cdot - 70$

$y = - 9 - \frac{11 x}{4}$

Cancel the common factor.

$\frac{1}{35} \cdot (35 x) = \frac{2}{35} \cdot - 70$

$y = - 9 - \frac{11 x}{4}$

Rewrite the expression.

$x = \frac{2}{35} \cdot - 70$

$y = - 9 - \frac{11 x}{4}$

$x = \frac{2}{35} \cdot - 70$

$y = - 9 - \frac{11 x}{4}$

$x = \frac{2}{35} \cdot - 70$

$y = - 9 - \frac{11 x}{4}$

$x = \frac{2}{35} \cdot - 70$

$y = - 9 - \frac{11 x}{4}$

Simplify the right side.

Simplify $\frac{2}{35} \cdot - 70$ .

Cancel the common factor of $35$ .

Factor $35$ out of $- 70$ .

$x = \frac{2}{35} \cdot (35 (- 2))$

$y = - 9 - \frac{11 x}{4}$

Cancel the common factor.

$x = \frac{2}{35} \cdot (35 \cdot - 2)$

$y = - 9 - \frac{11 x}{4}$

Rewrite the expression.

$x = 2 \cdot - 2$

$y = - 9 - \frac{11 x}{4}$

$x = 2 \cdot - 2$

$y = - 9 - \frac{11 x}{4}$

Multiply $2$ by $- 2$ .

$x = - 4$

$y = - 9 - \frac{11 x}{4}$

$x = - 4$

$y = - 9 - \frac{11 x}{4}$

$x = - 4$

$y = - 9 - \frac{11 x}{4}$

$x = - 4$

$y = - 9 - \frac{11 x}{4}$

$x = - 4$

$y = - 9 - \frac{11 x}{4}$

Step 4

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

Replace all occurrences of $x$ in $y = - 9 - \frac{11 x}{4}$ with $- 4$ .

$y = - 9 - \frac{11 (- 4)}{4}$

$x = - 4$

Simplify the right side.

Simplify $- 9 - \frac{11 (- 4)}{4}$ .

Simplify each term.

Cancel the common factor of $- 4$ and $4$ .

Factor $4$ out of $11 (- 4)$ .

$y = - 9 - \frac{4 (11 \cdot (- 1))}{4}$

$x = - 4$

Cancel the common factors.

Factor $4$ out of $4$ .

$y = - 9 - \frac{4 (11 \cdot (- 1))}{4 (1)}$

$x = - 4$

Cancel the common factor.

$y = - 9 - \frac{4 (11 \cdot (- 1))}{4 \cdot 1}$

$x = - 4$

Rewrite the expression.

$y = - 9 - \frac{11 \cdot (- 1)}{1}$

$x = - 4$

Divide $11 \cdot (- 1)$ by $1$ .

$y = - 9 - (11 \cdot (- 1))$

$x = - 4$

$y = - 9 - (11 \cdot (- 1))$

$x = - 4$

$y = - 9 - (11 \cdot (- 1))$

$x = - 4$

Multiply $- (11 \cdot (- 1))$ .

Multiply $11$ by $- 1$ .

$y = - 9 + 11$

$x = - 4$

Multiply $- 1$ by $- 11$ .

$y = - 9 + 11$

$x = - 4$

$y = - 9 + 11$

$x = - 4$

$y = - 9 + 11$

$x = - 4$

Add $- 9$ and $11$ .

$y = 2$

$x = - 4$

$y = 2$

$x = - 4$

$y = 2$

$x = - 4$

$y = 2$

$x = - 4$

Step 5

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

$(- 4, 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 4, 2)$

Equation Form:

$x = - 4, y = 2$

Step 7

Solve the System of Equations -4y-11x=36 20=-10x-10y

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