Determine if Linear 11x(y+8)=5-11y(3-x)

$11 x (y + 8) = 5 - 11 y (3 - x)$

Step 1

Solve the equation for $y$ .

Simplify $11 x (y + 8)$ .

Rewrite.

$0 + 0 + 11 x (y + 8) = 5 - 11 y (3 - x)$

Simplify by adding zeros.

$11 x (y + 8) = 5 - 11 y (3 - x)$

Apply the distributive property.

$11 x y + 11 x \cdot 8 = 5 - 11 y (3 - x)$

Multiply $8$ by $11$ .

$11 x y + 88 x = 5 - 11 y (3 - x)$

Simplify each term.

Apply the distributive property.

$11 x y + 88 x = 5 - 11 y \cdot 3 - 11 y (- x)$

Multiply $3$ by $- 11$ .

$11 x y + 88 x = 5 - 33 y - 11 y (- x)$

Rewrite using the commutative property of multiplication.

$11 x y + 88 x = 5 - 33 y - 11 \cdot - 1 y x$

Multiply $- 11$ by $- 1$ .

$11 x y + 88 x = 5 - 33 y + 11 y x$

Since $y$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$5 - 33 y + 11 y x = 11 x y + 88 x$

Move all terms containing $y$ to the left side of the equation.

Subtract $11 x y$ from both sides of the equation.

$5 - 33 y + 11 y x - 11 x y = 88 x$

Combine the opposite terms in $5 - 33 y + 11 y x - 11 x y$ .

Reorder the factors in the terms $11 y x$ and $- 11 x y$ .

$5 - 33 y + 11 x y - 11 x y = 88 x$

Subtract $11 x y$ from $11 x y$ .

$5 - 33 y + 0 = 88 x$

Add $5 - 33 y$ and $0$ .

$5 - 33 y = 88 x$

Subtract $5$ from both sides of the equation.

$- 33 y = 88 x - 5$

Divide each term in $- 33 y = 88 x - 5$ by $- 33$ and simplify.

Divide each term in $- 33 y = 88 x - 5$ by $- 33$ .

$\frac{- 33 y}{- 33} = \frac{88 x}{- 33} + \frac{- 5}{- 33}$

Simplify the left side.

Cancel the common factor of $- 33$ .

Cancel the common factor.

$\frac{- 33 y}{- 33} = \frac{88 x}{- 33} + \frac{- 5}{- 33}$

Divide $y$ by $1$ .

$y = \frac{88 x}{- 33} + \frac{- 5}{- 33}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $88$ and $- 33$ .

Factor $11$ out of $88 x$ .

$y = \frac{11 (8 x)}{- 33} + \frac{- 5}{- 33}$

Cancel the common factors.

Factor $11$ out of $- 33$ .

$y = \frac{11 (8 x)}{11 (- 3)} + \frac{- 5}{- 33}$

Cancel the common factor.

$y = \frac{11 (8 x)}{11 \cdot - 3} + \frac{- 5}{- 33}$

Rewrite the expression.

$y = \frac{8 x}{- 3} + \frac{- 5}{- 33}$

Move the negative in front of the fraction.

$y = - \frac{8 x}{3} + \frac{- 5}{- 33}$

Dividing two negative values results in a positive value.

$y = - \frac{8 x}{3} + \frac{5}{33}$

Step 2

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be $0$ or $1$ for each of its variables. In this case, the degree of variable $y$ is $1$ and the degree of variable $x$ is $1$ .

Linear

Determine if Linear 11x(y+8)=5-11y(3-x)

Related Questions

Support LCMGCF.com by disabling your adblocker.