Solve {l}{x-y+z=4}{3x=10}{x-4y+2z=6}

$$\left\{ \begin{array}{l}{ x - y + z = 4 }\\{ 3 x = 10 }\\{ x - 4 y + 2 z = 6 }\end{array} \right.$$

Solve for x, y, z

$$x = \frac{10}{3} = 3\frac{1}{3} \approx 3.333333333$$

$$y=-\frac{2}{3}\approx -0.666666667$$

$$z=0$$

Short Steps Using Substitution

Solve x-y+z=4 for x.

$$x=y-z+4$$

Substitute y-z+4 for x in the second and third equation.

$$3\left(y-z+4\right)=10 y-z+4-4y+2z=6$$

Solve these equations for y and z respectively.

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

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

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

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

$$z=0$$

Substitute 0 for z in the equation y=-\frac{2}{3}+z.

$$y=-\frac{2}{3}+0$$

Calculate y from y=-\frac{2}{3}+0.

$$y=-\frac{2}{3}$$

Substitute -\frac{2}{3} for y and 0 for z in the equation x=y-z+4.

$$x=-\frac{2}{3}-0+4$$

Calculate x from x=-\frac{2}{3}-0+4.

$$x=\frac{10}{3}$$

The system is now solved.

$$x=\frac{10}{3} y=-\frac{2}{3} z=0$$