Solve {l}{x+y+z=100}{x+z=75}{y+z=65}

$$\left. \begin{array} { l } { x + y + z = 100 } \\ { x + z = 75 } \\ { y + z = 65 } \end{array} \right.$$

Solve for x, y, z

$$x=35$$

$$y=25$$

$$z=40$$

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+z=75.

$$-y-z+100+z=75$$

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

$$y=25 z=-y+65$$

Substitute 25 for y in the equation z=-y+65.

$$z=-25+65$$

Calculate z from z=-25+65.

$$z=40$$

Substitute 25 for y and 40 for z in the equation x=-y-z+100.

$$x=-25-40+100$$

Calculate x from x=-25-40+100.

$$x=35$$

The system is now solved.

$$x=35 y=25 z=40$$