Determine if Linear 9x(y+2)=1-9y(4-x)

$9 x (y + 2) = 1 - 9 y (4 - x)$

Step 1

Solve the equation for $y$ .

Simplify $9 x (y + 2)$ .

Rewrite.

$0 + 0 + 9 x (y + 2) = 1 - 9 y (4 - x)$

Simplify by adding zeros.

$9 x (y + 2) = 1 - 9 y (4 - x)$

Apply the distributive property.

$9 x y + 9 x \cdot 2 = 1 - 9 y (4 - x)$

Multiply $2$ by $9$ .

$9 x y + 18 x = 1 - 9 y (4 - x)$

Simplify each term.

Apply the distributive property.

$9 x y + 18 x = 1 - 9 y \cdot 4 - 9 y (- x)$

Multiply $4$ by $- 9$ .

$9 x y + 18 x = 1 - 36 y - 9 y (- x)$

Rewrite using the commutative property of multiplication.

$9 x y + 18 x = 1 - 36 y - 9 \cdot - 1 y x$

Multiply $- 9$ by $- 1$ .

$9 x y + 18 x = 1 - 36 y + 9 y x$

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

$1 - 36 y + 9 y x = 9 x y + 18 x$

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

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

$1 - 36 y + 9 y x - 9 x y = 18 x$

Combine the opposite terms in $1 - 36 y + 9 y x - 9 x y$ .

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

$1 - 36 y + 9 x y - 9 x y = 18 x$

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

$1 - 36 y + 0 = 18 x$

Add $1 - 36 y$ and $0$ .

$1 - 36 y = 18 x$

Subtract $1$ from both sides of the equation.

$- 36 y = 18 x - 1$

Divide each term in $- 36 y = 18 x - 1$ by $- 36$ and simplify.

Divide each term in $- 36 y = 18 x - 1$ by $- 36$ .

$\frac{- 36 y}{- 36} = \frac{18 x}{- 36} + \frac{- 1}{- 36}$

Simplify the left side.

Cancel the common factor of $- 36$ .

Cancel the common factor.

$\frac{- 36 y}{- 36} = \frac{18 x}{- 36} + \frac{- 1}{- 36}$

Divide $y$ by $1$ .

$y = \frac{18 x}{- 36} + \frac{- 1}{- 36}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $18$ and $- 36$ .

Factor $18$ out of $18 x$ .

$y = \frac{18 (x)}{- 36} + \frac{- 1}{- 36}$

Cancel the common factors.

Factor $18$ out of $- 36$ .

$y = \frac{18 x}{18 \cdot - 2} + \frac{- 1}{- 36}$

Cancel the common factor.

$y = \frac{18 x}{18 \cdot - 2} + \frac{- 1}{- 36}$

Rewrite the expression.

$y = \frac{x}{- 2} + \frac{- 1}{- 36}$

Move the negative in front of the fraction.

$y = - \frac{x}{2} + \frac{- 1}{- 36}$

Dividing two negative values results in a positive value.

$y = - \frac{x}{2} + \frac{1}{36}$

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+2)=1-9y(4-x)

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