Solve {l}{5=3x-2y}{0=-x+8y-2z}{1y=-2y+3z}

$$\left. \begin{array} { l } { 5 = 3 x - 2 y } \\ { 0 = - x + 8 y - 2 z } \\ { 1 y = - 2 y + 3 z } \end{array} \right.$$

Solve for x, y, z

$$x = \frac{15}{8} = 1\frac{7}{8} = 1.875$$

$$y=\frac{5}{16}=0.3125$$

$$z=\frac{5}{16}=0.3125$$

Short Steps Using Substitution

Reorder the equations.

$$0=-x+8y-2z 5=3x-2y 1y=-2y+3z$$

Solve 0=-x+8y-2z for x.

$$x=8y-2z$$

Substitute 8y-2z for x in the equation 5=3x-2y.

$$5=3\left(8y-2z\right)-2y$$

Solve the second equation for y and the third equation for z.

$$y=\frac{5}{22}+\frac{3}{11}z z=y$$

Substitute \frac{5}{22}+\frac{3}{11}z for y in the equation z=y.

$$z=\frac{5}{22}+\frac{3}{11}z$$

Solve z=\frac{5}{22}+\frac{3}{11}z for z.

$$z=\frac{5}{16}$$

Substitute \frac{5}{16} for z in the equation y=\frac{5}{22}+\frac{3}{11}z.

$$y=\frac{5}{22}+\frac{3}{11}\times \frac{5}{16}$$

Calculate y from y=\frac{5}{22}+\frac{3}{11}\times \frac{5}{16}.

$$y=\frac{5}{16}$$

Substitute \frac{5}{16} for y and \frac{5}{16} for z in the equation x=8y-2z.

$$x=8\times \frac{5}{16}-2\times \frac{5}{16}$$

Calculate x from x=8\times \frac{5}{16}-2\times \frac{5}{16}.

$$x=\frac{15}{8}$$

The system is now solved.

$$x=\frac{15}{8} y=\frac{5}{16} z=\frac{5}{16}$$