Solve {l}{x+y+z=100}{x-y=2}{y-z=4}

$$\left. \begin{array} { l } { x + y + z = 100 } \\ { x - y = 2 } \\ { y - z = 4 } \end{array} \right.$$

Solve for x, y, z

$$x=36$$

$$y=34$$

$$z=30$$

Short Steps Using Substitution

Solve x+y+z=100 for x.

$$x=-y-z+100$$

Substitute -y-z+100 for x in the equation x-y=2.

$$-y-z+100-y=2$$

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

$$y=-\frac{1}{2}z+49 z=y-4$$

Substitute -\frac{1}{2}z+49 for y in the equation z=y-4.

$$z=-\frac{1}{2}z+49-4$$

Solve z=-\frac{1}{2}z+49-4 for z.

$$z=30$$

Substitute 30 for z in the equation y=-\frac{1}{2}z+49.

$$y=-\frac{1}{2}\times 30+49$$

Calculate y from y=-\frac{1}{2}\times 30+49.

$$y=34$$

Substitute 34 for y and 30 for z in the equation x=-y-z+100.

$$x=-34-30+100$$

Calculate x from x=-34-30+100.

$$x=36$$

The system is now solved.

$$x=36 y=34 z=30$$