Solve {c}{y+z=1}{y-z=0}{3y-6x+1=0}

$$\left. \begin{array} { c } { y + z = 1 } \\ { y - z = 0 } \\ { 3 y - 6 x + 1 = 0 } \end{array} \right.$$

Solve for y, z, x

$$x=\frac{5}{12}\approx 0.416666667$$

$$y=\frac{1}{2}=0.5$$

$$z=\frac{1}{2}=0.5$$

Short Steps Using Substitution

Solve y+z=1 for y.

$$y=-z+1$$

Substitute -z+1 for y in the second and third equation.

$$-z+1-z=0 3\left(-z+1\right)-6x+1=0$$

Solve these equations for z and x respectively.

$$z=\frac{1}{2} x=-\frac{1}{2}z+\frac{2}{3}$$

Substitute \frac{1}{2} for z in the equation x=-\frac{1}{2}z+\frac{2}{3}.

$$x=-\frac{1}{2}\times \frac{1}{2}+\frac{2}{3}$$

Calculate x from x=-\frac{1}{2}\times \frac{1}{2}+\frac{2}{3}.

$$x=\frac{5}{12}$$

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

$$y=-\frac{1}{2}+1$$

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

$$y=\frac{1}{2}$$

The system is now solved.

$$y=\frac{1}{2} z=\frac{1}{2} x=\frac{5}{12}$$