Solve {l}{4x+3y+z=-25}{x-3y+2z=10}{11x-2y+3z=-47}

$$\left. \begin{array}{l}{ 4 x + 3 y + z = - 25 }\\{ x - 3 y + 2 z = 10 }\\{ 11 x - 2 y + 3 z = - 47 }\end{array} \right.$$

Solve for x, y, z

$$x=-6$$

$$y=-2$$

$$z=5$$

Short Steps Using Substitution

Solve 4x+3y+z=-25 for z.

$$z=-4x-3y-25$$

Substitute -4x-3y-25 for z in the second and third equation.

$$x-3y+2\left(-4x-3y-25\right)=10 11x-2y+3\left(-4x-3y-25\right)=-47$$

Solve these equations for y and x respectively.

$$y=-\frac{7}{9}x-\frac{20}{3} x=-11y-28$$

Substitute -\frac{7}{9}x-\frac{20}{3} for y in the equation x=-11y-28.

$$x=-11\left(-\frac{7}{9}x-\frac{20}{3}\right)-28$$

Solve x=-11\left(-\frac{7}{9}x-\frac{20}{3}\right)-28 for x.

$$x=-6$$

Substitute -6 for x in the equation y=-\frac{7}{9}x-\frac{20}{3}.

$$y=-\frac{7}{9}\left(-6\right)-\frac{20}{3}$$

Calculate y from y=-\frac{7}{9}\left(-6\right)-\frac{20}{3}.

$$y=-2$$

Substitute -2 for y and -6 for x in the equation z=-4x-3y-25.

$$z=-4\left(-6\right)-3\left(-2\right)-25$$

Calculate z from z=-4\left(-6\right)-3\left(-2\right)-25.

$$z=5$$

The system is now solved.

$$x=-6 y=-2 z=5$$