Solve {l}{2y-z=5}{4x-y+3z=-8}{3y=9}

$$\left\{ \begin{array}{l}{ 2 y - z = 5 }\\{ 4 x - y + 3 z = - 8 }\\{ 3 y = 9 }\end{array} \right.$$

Solve for y, z, x

$$x=-2$$

$$y=3$$

$$z=1$$

Solution Steps

Consider the third equation. Divide both sides by 3.

$$y=\frac{9}{3}$$

Divide 9 by 3 to get 3.

$$y=3$$

Consider the first equation. Insert the known values of variables into the equation.

$$2\times 3-z=5$$

Multiply 2 and 3 to get 6.

$$6-z=5$$

Subtract 6 from both sides.

$$-z=5-6$$

Subtract 6 from 5 to get -1.

$$-z=-1$$

Divide both sides by -1.

$$z=\frac{-1}{-1}$$

Divide -1 by -1 to get 1.

$$z=1$$

Consider the second equation. Insert the known values of variables into the equation.

$$4x-3+3\times 1=-8$$

Do the multiplications.

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

Add -3 and 3 to get 0.

$$4x=-8$$

Divide both sides by 4.

$$x=\frac{-8}{4}$$

Divide -8 by 4 to get -2.

$$x=-2$$

The system is now solved.

$$y=3 z=1 x=-2$$