Determine if Linear 8x(y+5)=9-8y(2-x)

$8 x (y + 5) = 9 - 8 y (2 - x)$

Step 1

Solve the equation for $y$ .

Simplify $8 x (y + 5)$ .

Rewrite.

$0 + 0 + 8 x (y + 5) = 9 - 8 y (2 - x)$

Simplify by adding zeros.

$8 x (y + 5) = 9 - 8 y (2 - x)$

Apply the distributive property.

$8 x y + 8 x \cdot 5 = 9 - 8 y (2 - x)$

Multiply $5$ by $8$ .

$8 x y + 40 x = 9 - 8 y (2 - x)$

Simplify each term.

Apply the distributive property.

$8 x y + 40 x = 9 - 8 y \cdot 2 - 8 y (- x)$

Multiply $2$ by $- 8$ .

$8 x y + 40 x = 9 - 16 y - 8 y (- x)$

Rewrite using the commutative property of multiplication.

$8 x y + 40 x = 9 - 16 y - 8 \cdot - 1 y x$

Multiply $- 8$ by $- 1$ .

$8 x y + 40 x = 9 - 16 y + 8 y x$

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

$9 - 16 y + 8 y x = 8 x y + 40 x$

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

Subtract $8 x y$ from both sides of the equation.

$9 - 16 y + 8 y x - 8 x y = 40 x$

Combine the opposite terms in $9 - 16 y + 8 y x - 8 x y$ .

Reorder the factors in the terms $8 y x$ and $- 8 x y$ .

$9 - 16 y + 8 x y - 8 x y = 40 x$

Subtract $8 x y$ from $8 x y$ .

$9 - 16 y + 0 = 40 x$

Add $9 - 16 y$ and $0$ .

$9 - 16 y = 40 x$

Subtract $9$ from both sides of the equation.

$- 16 y = 40 x - 9$

Divide each term in $- 16 y = 40 x - 9$ by $- 16$ and simplify.

Divide each term in $- 16 y = 40 x - 9$ by $- 16$ .

$\frac{- 16 y}{- 16} = \frac{40 x}{- 16} + \frac{- 9}{- 16}$

Simplify the left side.

Cancel the common factor of $- 16$ .

Cancel the common factor.

$\frac{- 16 y}{- 16} = \frac{40 x}{- 16} + \frac{- 9}{- 16}$

Divide $y$ by $1$ .

$y = \frac{40 x}{- 16} + \frac{- 9}{- 16}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $40$ and $- 16$ .

Factor $8$ out of $40 x$ .

$y = \frac{8 (5 x)}{- 16} + \frac{- 9}{- 16}$

Cancel the common factors.

Factor $8$ out of $- 16$ .

$y = \frac{8 (5 x)}{8 (- 2)} + \frac{- 9}{- 16}$

Cancel the common factor.

$y = \frac{8 (5 x)}{8 \cdot - 2} + \frac{- 9}{- 16}$

Rewrite the expression.

$y = \frac{5 x}{- 2} + \frac{- 9}{- 16}$

Move the negative in front of the fraction.

$y = - \frac{5 x}{2} + \frac{- 9}{- 16}$

Dividing two negative values results in a positive value.

$y = - \frac{5 x}{2} + \frac{9}{16}$

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 8x(y+5)=9-8y(2-x)

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