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

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

Solve for y

$$y=\frac{4-5z}{3}$$

Steps for Solving Linear Equation

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

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

Combine 2y and y to get 3y.

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

Combine 2z and 3z to get 5z.

$$-6+3y+5z=-2$$

Add 6 to both sides.

$$3y+5z=-2+6$$

Add -2 and 6 to get 4.

$$3y+5z=4$$

Subtract 5z from both sides.

$$3y=4-5z$$

Divide both sides by 3.

$$\frac{3y}{3}=\frac{4-5z}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$y=\frac{4-5z}{3}$$

Solve for z

$$z=\frac{4-3y}{5}$$

Steps for Solving Linear Equation

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

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

Combine 2y and y to get 3y.

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

Combine 2z and 3z to get 5z.

$$-6+3y+5z=-2$$

Add 6 to both sides.

$$3y+5z=-2+6$$

Add -2 and 6 to get 4.

$$3y+5z=4$$

Subtract 3y from both sides.

$$5z=4-3y$$

Divide both sides by 5.

$$\frac{5z}{5}=\frac{4-3y}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$z=\frac{4-3y}{5}$$