Solve 4z+3y=2(y+3z)

$$4z+3y=2(y+3z)$$

Solve for y

$$y=2z$$

Solution Steps

Use the distributive property to multiply 2 by y+3z.

$$4z+3y=2y+6z$$

Subtract 2y from both sides.

$$4z+3y-2y=6z$$

Combine 3y and -2y to get y.

$$4z+y=6z$$

Subtract 4z from both sides.

$$y=6z-4z$$

Combine 6z and -4z to get 2z.

$$y=2z$$

Solve for z

$$z=\frac{y}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2 by y+3z.

$$4z+3y=2y+6z$$

Subtract 6z from both sides.

$$4z+3y-6z=2y$$

Combine 4z and -6z to get -2z.

$$-2z+3y=2y$$

Subtract 3y from both sides.

$$-2z=2y-3y$$

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

$$-2z=-y$$

Divide both sides by -2.

$$\frac{-2z}{-2}=-\frac{y}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$z=-\frac{y}{-2}$$

Divide -y by -2.

$$z=\frac{y}{2}$$