Solve {l}{1.7x=y+z}{2.5y=x+z}{1.5z=x+y}

$$\left. \begin{array} { l } { 1.7 x = y + z } \\ { 2.5 y = x + z } \\ { 1.5 z = x + y } \end{array} \right.$$

Solve for x, y, z

$$x=0$$

$$y=0$$

$$z=0$$

Short Steps Using Substitution

Solve 1.7x=y+z for y.

$$y=1.7x-z$$

Substitute 1.7x-z for y in the second and third equation.

$$2.5\left(1.7x-z\right)=x+z 1.5z=x+1.7x-z$$

Solve these equations for x and z respectively.

$$x=\frac{14}{13}z z=1.08x$$

Substitute \frac{14}{13}z for x in the equation z=1.08x.

$$z=1.08\times \frac{14}{13}z$$

Solve z=1.08\times \frac{14}{13}z for z.

$$z=0$$

Substitute 0 for z in the equation x=\frac{14}{13}z.

$$x=\frac{14}{13}\times 0$$

Calculate x from x=\frac{14}{13}\times 0.

$$x=0$$

Substitute 0 for x and 0 for z in the equation y=1.7x-z.

$$y=1.7\times 0-0$$

Calculate y from y=1.7\times 0-0.

$$y=0$$

The system is now solved.

$$x=0 y=0 z=0$$