Solve {l}{x+y+z=70}{x-y=40}{y-z=30}

$$\left. \begin{array} { l } { x + y + z = 70 } \\ { x - y = 40 } \\ { y - z = 30 } \end{array} \right.$$

Solve for x, y, z

$$x=60$$

$$y=20$$

$$z=-10$$

Short Steps Using Substitution

Solve x+y+z=70 for x.

$$x=-y-z+70$$

Substitute -y-z+70 for x in the equation x-y=40.

$$-y-z+70-y=40$$

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

$$y=-\frac{1}{2}z+15 z=y-30$$

Substitute -\frac{1}{2}z+15 for y in the equation z=y-30.

$$z=-\frac{1}{2}z+15-30$$

Solve z=-\frac{1}{2}z+15-30 for z.

$$z=-10$$

Substitute -10 for z in the equation y=-\frac{1}{2}z+15.

$$y=-\frac{1}{2}\left(-10\right)+15$$

Calculate y from y=-\frac{1}{2}\left(-10\right)+15.

$$y=20$$

Substitute 20 for y and -10 for z in the equation x=-y-z+70.

$$x=-20-\left(-10\right)+70$$

Calculate x from x=-20-\left(-10\right)+70.

$$x=60$$

The system is now solved.

$$x=60 y=20 z=-10$$