Solve {l}{x+2y=25}{3y+z=20}{z+3x=15}

$$\left. \begin{array} { l } { x + 2 y = 25 } \\ { 3 y + z = 20 } \\ { z + 3 x = 15 } \end{array} \right.$$

Solve for x, y, z

$$x = \frac{65}{9} = 7\frac{2}{9} \approx 7.222222222$$

$$y = \frac{80}{9} = 8\frac{8}{9} \approx 8.888888889$$

$$z = -\frac{20}{3} = -6\frac{2}{3} \approx -6.666666667$$

Short Steps Using Substitution

Solve x+2y=25 for x.

$$x=-2y+25$$

Substitute -2y+25 for x in the equation z+3x=15.

$$z+3\left(-2y+25\right)=15$$

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

$$y=-\frac{1}{3}z+\frac{20}{3} z=-60+6y$$

Substitute -\frac{1}{3}z+\frac{20}{3} for y in the equation z=-60+6y.

$$z=-60+6\left(-\frac{1}{3}z+\frac{20}{3}\right)$$

Solve z=-60+6\left(-\frac{1}{3}z+\frac{20}{3}\right) for z.

$$z=-\frac{20}{3}$$

Substitute -\frac{20}{3} for z in the equation y=-\frac{1}{3}z+\frac{20}{3}.

$$y=-\frac{1}{3}\left(-\frac{20}{3}\right)+\frac{20}{3}$$

Calculate y from y=-\frac{1}{3}\left(-\frac{20}{3}\right)+\frac{20}{3}.

$$y=\frac{80}{9}$$

Substitute \frac{80}{9} for y in the equation x=-2y+25.

$$x=-2\times \frac{80}{9}+25$$

Calculate x from x=-2\times \frac{80}{9}+25.

$$x=\frac{65}{9}$$

The system is now solved.

$$x=\frac{65}{9} y=\frac{80}{9} z=-\frac{20}{3}$$