Determine if Linear 9x(y+4)=1-9y(6-x)

$9 x (y + 4) = 1 - 9 y (6 - x)$

Step 1

Solve the equation for $y$ .

Simplify $9 x (y + 4)$ .

Rewrite.

$0 + 0 + 9 x (y + 4) = 1 - 9 y (6 - x)$

Simplify by adding zeros.

$9 x (y + 4) = 1 - 9 y (6 - x)$

Apply the distributive property.

$9 x y + 9 x \cdot 4 = 1 - 9 y (6 - x)$

Multiply $4$ by $9$ .

$9 x y + 36 x = 1 - 9 y (6 - x)$

Simplify each term.

Apply the distributive property.

$9 x y + 36 x = 1 - 9 y \cdot 6 - 9 y (- x)$

Multiply $6$ by $- 9$ .

$9 x y + 36 x = 1 - 54 y - 9 y (- x)$

Rewrite using the commutative property of multiplication.

$9 x y + 36 x = 1 - 54 y - 9 \cdot - 1 y x$

Multiply $- 9$ by $- 1$ .

$9 x y + 36 x = 1 - 54 y + 9 y x$

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

$1 - 54 y + 9 y x = 9 x y + 36 x$

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

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

$1 - 54 y + 9 y x - 9 x y = 36 x$

Combine the opposite terms in $1 - 54 y + 9 y x - 9 x y$ .

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

$1 - 54 y + 9 x y - 9 x y = 36 x$

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

$1 - 54 y + 0 = 36 x$

Add $1 - 54 y$ and $0$ .

$1 - 54 y = 36 x$

Subtract $1$ from both sides of the equation.

$- 54 y = 36 x - 1$

Divide each term in $- 54 y = 36 x - 1$ by $- 54$ and simplify.

Divide each term in $- 54 y = 36 x - 1$ by $- 54$ .

$\frac{- 54 y}{- 54} = \frac{36 x}{- 54} + \frac{- 1}{- 54}$

Simplify the left side.

Cancel the common factor of $- 54$ .

Cancel the common factor.

$\frac{- 54 y}{- 54} = \frac{36 x}{- 54} + \frac{- 1}{- 54}$

Divide $y$ by $1$ .

$y = \frac{36 x}{- 54} + \frac{- 1}{- 54}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $36$ and $- 54$ .

Factor $18$ out of $36 x$ .

$y = \frac{18 (2 x)}{- 54} + \frac{- 1}{- 54}$

Cancel the common factors.

Factor $18$ out of $- 54$ .

$y = \frac{18 (2 x)}{18 (- 3)} + \frac{- 1}{- 54}$

Cancel the common factor.

$y = \frac{18 (2 x)}{18 \cdot - 3} + \frac{- 1}{- 54}$

Rewrite the expression.

$y = \frac{2 x}{- 3} + \frac{- 1}{- 54}$

Move the negative in front of the fraction.

$y = - \frac{2 x}{3} + \frac{- 1}{- 54}$

Dividing two negative values results in a positive value.

$y = - \frac{2 x}{3} + \frac{1}{54}$

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+4)=1-9y(6-x)

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