Solve {l}{x+y+z=35}{2x=y+5}{1/3y=1/2z}

$$\left\{ \begin{array} { l } { x + y + z = 35 } \\ { 2 x = y + 5 } \\ { \frac { 1 } { 3 } y = \frac { 1 } { 2 } z } \end{array} \right.$$

Solve for x, y, z

$$x=10$$

$$y=15$$

$$z=10$$

Short Steps Using Substitution

Solve x+y+z=35 for x.

$$x=-y-z+35$$

Substitute -y-z+35 for x in the equation 2x=y+5.

$$2\left(-y-z+35\right)=y+5$$

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

$$y=-\frac{2}{3}z+\frac{65}{3} z=\frac{2}{3}y$$

Substitute -\frac{2}{3}z+\frac{65}{3} for y in the equation z=\frac{2}{3}y.

$$z=\frac{2}{3}\left(-\frac{2}{3}z+\frac{65}{3}\right)$$

Solve z=\frac{2}{3}\left(-\frac{2}{3}z+\frac{65}{3}\right) for z.

$$z=10$$

Substitute 10 for z in the equation y=-\frac{2}{3}z+\frac{65}{3}.

$$y=-\frac{2}{3}\times 10+\frac{65}{3}$$

Calculate y from y=-\frac{2}{3}\times 10+\frac{65}{3}.

$$y=15$$

Substitute 15 for y and 10 for z in the equation x=-y-z+35.

$$x=-15-10+35$$

Calculate x from x=-15-10+35.

$$x=10$$

The system is now solved.

$$x=10 y=15 z=10$$