Solve {l}{x+7y-3z=-6}{2x-14y+5z=12}{3x+7y-2z=-3}

$$\left. \begin{array}{l}{ x + 7 y - 3 z = - 6 }\\{ 2 x - 14 y + 5 z = 12 }\\{ 3 x + 7 y - 2 z = - 3 }\end{array} \right.$$

Solve for x, y, z

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

$$y=-\frac{1}{14}\approx -0.071428571$$

$$z=2$$

Short Steps Using Substitution

Solve x+7y-3z=-6 for x.

$$x=-7y+3z-6$$

Substitute -7y+3z-6 for x in the second and third equation.

$$2\left(-7y+3z-6\right)-14y+5z=12 3\left(-7y+3z-6\right)+7y-2z=-3$$

Solve these equations for y and z respectively.

$$y=\frac{11}{28}z-\frac{6}{7} z=2y+\frac{15}{7}$$

Substitute \frac{11}{28}z-\frac{6}{7} for y in the equation z=2y+\frac{15}{7}.

$$z=2\left(\frac{11}{28}z-\frac{6}{7}\right)+\frac{15}{7}$$

Solve z=2\left(\frac{11}{28}z-\frac{6}{7}\right)+\frac{15}{7} for z.

$$z=2$$

Substitute 2 for z in the equation y=\frac{11}{28}z-\frac{6}{7}.

$$y=\frac{11}{28}\times 2-\frac{6}{7}$$

Calculate y from y=\frac{11}{28}\times 2-\frac{6}{7}.

$$y=-\frac{1}{14}$$

Substitute -\frac{1}{14} for y and 2 for z in the equation x=-7y+3z-6.

$$x=-7\left(-\frac{1}{14}\right)+3\times 2-6$$

Calculate x from x=-7\left(-\frac{1}{14}\right)+3\times 2-6.

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

The system is now solved.

$$x=\frac{1}{2} y=-\frac{1}{14} z=2$$