Determine if Linear 2x(y+6)=1-2y(9-x)

$2 x (y + 6) = 1 - 2 y (9 - x)$

Step 1

Solve the equation for $y$ .

Simplify $2 x (y + 6)$ .

Rewrite.

$0 + 0 + 2 x (y + 6) = 1 - 2 y (9 - x)$

Simplify by adding zeros.

$2 x (y + 6) = 1 - 2 y (9 - x)$

Apply the distributive property.

$2 x y + 2 x \cdot 6 = 1 - 2 y (9 - x)$

Multiply $6$ by $2$ .

$2 x y + 12 x = 1 - 2 y (9 - x)$

Simplify each term.

Apply the distributive property.

$2 x y + 12 x = 1 - 2 y \cdot 9 - 2 y (- x)$

Multiply $9$ by $- 2$ .

$2 x y + 12 x = 1 - 18 y - 2 y (- x)$

Rewrite using the commutative property of multiplication.

$2 x y + 12 x = 1 - 18 y - 2 \cdot - 1 y x$

Multiply $- 2$ by $- 1$ .

$2 x y + 12 x = 1 - 18 y + 2 y x$

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

$1 - 18 y + 2 y x = 2 x y + 12 x$

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

Subtract $2 x y$ from both sides of the equation.

$1 - 18 y + 2 y x - 2 x y = 12 x$

Combine the opposite terms in $1 - 18 y + 2 y x - 2 x y$ .

Reorder the factors in the terms $2 y x$ and $- 2 x y$ .

$1 - 18 y + 2 x y - 2 x y = 12 x$

Subtract $2 x y$ from $2 x y$ .

$1 - 18 y + 0 = 12 x$

Add $1 - 18 y$ and $0$ .

$1 - 18 y = 12 x$

Subtract $1$ from both sides of the equation.

$- 18 y = 12 x - 1$

Divide each term in $- 18 y = 12 x - 1$ by $- 18$ and simplify.

Divide each term in $- 18 y = 12 x - 1$ by $- 18$ .

$\frac{- 18 y}{- 18} = \frac{12 x}{- 18} + \frac{- 1}{- 18}$

Simplify the left side.

Cancel the common factor of $- 18$ .

Cancel the common factor.

$\frac{- 18 y}{- 18} = \frac{12 x}{- 18} + \frac{- 1}{- 18}$

Divide $y$ by $1$ .

$y = \frac{12 x}{- 18} + \frac{- 1}{- 18}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $12$ and $- 18$ .

Factor $6$ out of $12 x$ .

$y = \frac{6 (2 x)}{- 18} + \frac{- 1}{- 18}$

Cancel the common factors.

Factor $6$ out of $- 18$ .

$y = \frac{6 (2 x)}{6 (- 3)} + \frac{- 1}{- 18}$

Cancel the common factor.

$y = \frac{6 (2 x)}{6 \cdot - 3} + \frac{- 1}{- 18}$

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Dividing two negative values results in a positive value.

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

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 2x(y+6)=1-2y(9-x)

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