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

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

Solve for x, y, z

$$x=-1$$

$$y=2$$

$$z=\frac{1}{2}=0.5$$

Short Steps Using Substitution

Solve 3x+y-4z=-3 for y.

$$y=-3x+4z-3$$

Substitute -3x+4z-3 for y in the second and third equation.

$$5x-2\left(-3x+4z-3\right)+8z=-5 2x+3\left(-3x+4z-3\right)-2z=3$$

Solve these equations for x and z respectively.

$$x=-1 z=\frac{7}{10}x+\frac{6}{5}$$

Substitute -1 for x in the equation z=\frac{7}{10}x+\frac{6}{5}.

$$z=\frac{7}{10}\left(-1\right)+\frac{6}{5}$$

Calculate z from z=\frac{7}{10}\left(-1\right)+\frac{6}{5}.

$$z=\frac{1}{2}$$

Substitute -1 for x and \frac{1}{2} for z in the equation y=-3x+4z-3.

$$y=-3\left(-1\right)+4\times \frac{1}{2}-3$$

Calculate y from y=-3\left(-1\right)+4\times \frac{1}{2}-3.

$$y=2$$

The system is now solved.

$$x=-1 y=2 z=\frac{1}{2}$$