Determine if Linear 9x(y+3)=4-9y(11-x)

$9 x (y + 3) = 4 - 9 y (11 - x)$

Step 1

Solve the equation for $y$ .

Simplify $9 x (y + 3)$ .

Rewrite.

$0 + 0 + 9 x (y + 3) = 4 - 9 y (11 - x)$

Simplify by adding zeros.

$9 x (y + 3) = 4 - 9 y (11 - x)$

Apply the distributive property.

$9 x y + 9 x \cdot 3 = 4 - 9 y (11 - x)$

Multiply $3$ by $9$ .

$9 x y + 27 x = 4 - 9 y (11 - x)$

Simplify each term.

Apply the distributive property.

$9 x y + 27 x = 4 - 9 y \cdot 11 - 9 y (- x)$

Multiply $11$ by $- 9$ .

$9 x y + 27 x = 4 - 99 y - 9 y (- x)$

Rewrite using the commutative property of multiplication.

$9 x y + 27 x = 4 - 99 y - 9 \cdot - 1 y x$

Multiply $- 9$ by $- 1$ .

$9 x y + 27 x = 4 - 99 y + 9 y x$

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

$4 - 99 y + 9 y x = 9 x y + 27 x$

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

Subtract $9 x y$ from both sides of the equation.

$4 - 99 y + 9 y x - 9 x y = 27 x$

Combine the opposite terms in $4 - 99 y + 9 y x - 9 x y$ .

Reorder the factors in the terms $9 y x$ and $- 9 x y$ .

$4 - 99 y + 9 x y - 9 x y = 27 x$

Subtract $9 x y$ from $9 x y$ .

$4 - 99 y + 0 = 27 x$

Add $4 - 99 y$ and $0$ .

$4 - 99 y = 27 x$

Subtract $4$ from both sides of the equation.

$- 99 y = 27 x - 4$

Divide each term in $- 99 y = 27 x - 4$ by $- 99$ and simplify.

Divide each term in $- 99 y = 27 x - 4$ by $- 99$ .

$\frac{- 99 y}{- 99} = \frac{27 x}{- 99} + \frac{- 4}{- 99}$

Simplify the left side.

Cancel the common factor of $- 99$ .

Cancel the common factor.

$\frac{- 99 y}{- 99} = \frac{27 x}{- 99} + \frac{- 4}{- 99}$

Divide $y$ by $1$ .

$y = \frac{27 x}{- 99} + \frac{- 4}{- 99}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $27$ and $- 99$ .

Factor $9$ out of $27 x$ .

$y = \frac{9 (3 x)}{- 99} + \frac{- 4}{- 99}$

Cancel the common factors.

Factor $9$ out of $- 99$ .

$y = \frac{9 (3 x)}{9 (- 11)} + \frac{- 4}{- 99}$

Cancel the common factor.

$y = \frac{9 (3 x)}{9 \cdot - 11} + \frac{- 4}{- 99}$

Rewrite the expression.

$y = \frac{3 x}{- 11} + \frac{- 4}{- 99}$

Move the negative in front of the fraction.

$y = - \frac{3 x}{11} + \frac{- 4}{- 99}$

Dividing two negative values results in a positive value.

$y = - \frac{3 x}{11} + \frac{4}{99}$

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 9x(y+3)=4-9y(11-x)

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