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

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

Solve for z, y, x

$$x=-2$$

$$y=1$$

$$z=3$$

Solution Steps

Consider the first equation. Divide both sides by 3.

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

Divide 9 by 3 to get 3.

$$z=3$$

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

$$-y+2\times 3=5$$

Multiply 2 and 3 to get 6.

$$-y+6=5$$

Subtract 6 from both sides.

$$-y=5-6$$

Subtract 6 from 5 to get -1.

$$-y=-1$$

Divide both sides by -1.

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

Divide -1 by -1 to get 1.

$$y=1$$

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

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

Do the multiplications.

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

Subtract 3 from 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.

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