Solve {l}{x=3z}{3x-y+2z=17}{2x-3y=-3}{}

$$\left. \begin{array} { l } { x = 3 z } \\ { 3 x - y + 2 z = 17 } \\ { 2 x - 3 y = - 3 } \\ { } \end{array} \right.$$

Solve for x, z, y

$$x=6$$

$$y=5$$

$$z=2$$

Short Steps Using Substitution

Substitute 3z for x in the second and third equation.

$$3\times 3z-y+2z=17 2\times 3z-3y=-3$$

Solve these equations for z and y respectively.

$$z=\frac{17}{11}+\frac{1}{11}y y=1+2z$$

Substitute \frac{17}{11}+\frac{1}{11}y for z in the equation y=1+2z.

$$y=1+2\left(\frac{17}{11}+\frac{1}{11}y\right)$$

Solve y=1+2\left(\frac{17}{11}+\frac{1}{11}y\right) for y.

$$y=5$$

Substitute 5 for y in the equation z=\frac{17}{11}+\frac{1}{11}y.

$$z=\frac{17}{11}+\frac{1}{11}\times 5$$

Calculate z from z=\frac{17}{11}+\frac{1}{11}\times 5.

$$z=2$$

Substitute 2 for z in the equation x=3z.

$$x=3\times 2$$

Calculate x from x=3\times 2.

$$x=6$$

The system is now solved.

$$x=6 z=2 y=5$$