Solve 2-(3y+4x)=4(x-y)

$$2 - ( 3 y + 4 x ) = 4 ( x - y )$$

Solve for x

$$x=\frac{y+2}{8}$$

Steps for Solving Linear Equation

To find the opposite of 3y+4x, find the opposite of each term.

$$2-3y-4x=4\left(x-y\right)$$

Use the distributive property to multiply 4 by x-y.

$$2-3y-4x=4x-4y$$

Subtract 4x from both sides.

$$2-3y-4x-4x=-4y$$

Combine -4x and -4x to get -8x.

$$2-3y-8x=-4y$$

Subtract 2 from both sides.

$$-3y-8x=-4y-2$$

Add 3y to both sides.

$$-8x=-4y-2+3y$$

Combine -4y and 3y to get -y.

$$-8x=-y-2$$

Divide both sides by -8.

$$\frac{-8x}{-8}=\frac{-y-2}{-8}$$

Dividing by -8 undoes the multiplication by -8.

$$x=\frac{-y-2}{-8}$$

Divide -y-2 by -8.

$$x=\frac{y}{8}+\frac{1}{4}$$

Solve for y

$$y=8x-2$$

Solution Steps

To find the opposite of 3y+4x, find the opposite of each term.

$$2-3y-4x=4\left(x-y\right)$$

Use the distributive property to multiply 4 by x-y.

$$2-3y-4x=4x-4y$$

Add 4y to both sides.

$$2-3y-4x+4y=4x$$

Combine -3y and 4y to get y.

$$2+y-4x=4x$$

Subtract 2 from both sides.

$$y-4x=4x-2$$

Add 4x to both sides.

$$y=4x-2+4x$$

Combine 4x and 4x to get 8x.

$$y=8x-2$$