Solve 2x(y-1)+4y(4-x)=x-y

$$2 x ( y - 1 ) + 4 y ( 4 - x ) = x - y$$

Solve for x

$$x=\frac{17y}{2y+3}$$

$$y\neq -\frac{3}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x by y-1.

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

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

$$2xy-2x+16y-4yx=x-y$$

Combine 2xy and -4yx to get -2xy.

$$-2xy-2x+16y=x-y$$

Subtract x from both sides.

$$-2xy-2x+16y-x=-y$$

Combine -2x and -x to get -3x.

$$-2xy-3x+16y=-y$$

Subtract 16y from both sides.

$$-2xy-3x=-y-16y$$

Combine -y and -16y to get -17y.

$$-2xy-3x=-17y$$

Combine all terms containing x.

$$\left(-2y-3\right)x=-17y$$

Divide both sides by -2y-3.

$$\frac{\left(-2y-3\right)x}{-2y-3}=-\frac{17y}{-2y-3}$$

Dividing by -2y-3 undoes the multiplication by -2y-3.

$$x=-\frac{17y}{-2y-3}$$

Divide -17y by -2y-3.

$$x=\frac{17y}{2y+3}$$

Solve for y

$$y=\frac{3x}{17-2x}$$

$$x\neq \frac{17}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x by y-1.

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

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

$$2xy-2x+16y-4yx=x-y$$

Combine 2xy and -4yx to get -2xy.

$$-2xy-2x+16y=x-y$$

Add y to both sides.

$$-2xy-2x+16y+y=x$$

Combine 16y and y to get 17y.

$$-2xy-2x+17y=x$$

Add 2x to both sides.

$$-2xy+17y=x+2x$$

Combine x and 2x to get 3x.

$$-2xy+17y=3x$$

Combine all terms containing y.

$$\left(-2x+17\right)y=3x$$

The equation is in standard form.

$$\left(17-2x\right)y=3x$$

Divide both sides by -2x+17.

$$\frac{\left(17-2x\right)y}{17-2x}=\frac{3x}{17-2x}$$

Dividing by -2x+17 undoes the multiplication by -2x+17.

$$y=\frac{3x}{17-2x}$$