Solve {r}{x+2y=4}{y-z=0}{x+3y-2z=5}

$$\left. \begin{array} { r } { x + 2 y = 4 } \\ { y - z = 0 } \\ { x + 3 y - 2 z = 5 } \end{array} \right.$$

Solve for x, y, z

$$x=6$$

$$y=-1$$

$$z=-1$$

Short Steps Using Substitution

Solve x+2y=4 for x.

$$x=4-2y$$

Substitute 4-2y for x in the equation x+3y-2z=5.

$$4-2y+3y-2z=5$$

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

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

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

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

Solve z=-\frac{1}{2}+\frac{1}{2}z for z.

$$z=-1$$

Substitute -1 for z in the equation y=z.

$$y=-1$$

Substitute -1 for y in the equation x=4-2y.

$$x=4-2\left(-1\right)$$

Calculate x from x=4-2\left(-1\right).

$$x=6$$

The system is now solved.

$$x=6 y=-1 z=-1$$