Determine if Linear 8x(y+4)=3-8y(6-x)

$8 x (y + 4) = 3 - 8 y (6 - x)$

Step 1

Solve the equation for $y$ .

Simplify $8 x (y + 4)$ .

Rewrite.

$0 + 0 + 8 x (y + 4) = 3 - 8 y (6 - x)$

Simplify by adding zeros.

$8 x (y + 4) = 3 - 8 y (6 - x)$

Apply the distributive property.

$8 x y + 8 x \cdot 4 = 3 - 8 y (6 - x)$

Multiply $4$ by $8$ .

$8 x y + 32 x = 3 - 8 y (6 - x)$

Simplify each term.

Apply the distributive property.

$8 x y + 32 x = 3 - 8 y \cdot 6 - 8 y (- x)$

Multiply $6$ by $- 8$ .

$8 x y + 32 x = 3 - 48 y - 8 y (- x)$

Rewrite using the commutative property of multiplication.

$8 x y + 32 x = 3 - 48 y - 8 \cdot - 1 y x$

Multiply $- 8$ by $- 1$ .

$8 x y + 32 x = 3 - 48 y + 8 y x$

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

$3 - 48 y + 8 y x = 8 x y + 32 x$

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

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

$3 - 48 y + 8 y x - 8 x y = 32 x$

Combine the opposite terms in $3 - 48 y + 8 y x - 8 x y$ .

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

$3 - 48 y + 8 x y - 8 x y = 32 x$

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

$3 - 48 y + 0 = 32 x$

Add $3 - 48 y$ and $0$ .

$3 - 48 y = 32 x$

Subtract $3$ from both sides of the equation.

$- 48 y = 32 x - 3$

Divide each term in $- 48 y = 32 x - 3$ by $- 48$ and simplify.

Divide each term in $- 48 y = 32 x - 3$ by $- 48$ .

$\frac{- 48 y}{- 48} = \frac{32 x}{- 48} + \frac{- 3}{- 48}$

Simplify the left side.

Cancel the common factor of $- 48$ .

Cancel the common factor.

$\frac{- 48 y}{- 48} = \frac{32 x}{- 48} + \frac{- 3}{- 48}$

Divide $y$ by $1$ .

$y = \frac{32 x}{- 48} + \frac{- 3}{- 48}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $32$ and $- 48$ .

Factor $16$ out of $32 x$ .

$y = \frac{16 (2 x)}{- 48} + \frac{- 3}{- 48}$

Cancel the common factors.

Factor $16$ out of $- 48$ .

$y = \frac{16 (2 x)}{16 (- 3)} + \frac{- 3}{- 48}$

Cancel the common factor.

$y = \frac{16 (2 x)}{16 \cdot - 3} + \frac{- 3}{- 48}$

Rewrite the expression.

$y = \frac{2 x}{- 3} + \frac{- 3}{- 48}$

Move the negative in front of the fraction.

$y = - \frac{2 x}{3} + \frac{- 3}{- 48}$

Cancel the common factor of $- 3$ and $- 48$ .

Factor $- 3$ out of $- 3$ .

$y = - \frac{2 x}{3} + \frac{- 3 (1)}{- 48}$

Cancel the common factors.

Factor $- 3$ out of $- 48$ .

$y = - \frac{2 x}{3} + \frac{- 3 \cdot 1}{- 3 \cdot 16}$

Cancel the common factor.

$y = - \frac{2 x}{3} + \frac{- 3 \cdot 1}{- 3 \cdot 16}$

Rewrite the expression.

$y = - \frac{2 x}{3} + \frac{1}{16}$

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+4)=3-8y(6-x)

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