Solve {l}{x+2y=-5}{y-3z=-11}{-2x-6y+5z=-1}

$$\left\{ \begin{array}{l}{ x + 2 y = - 5 }\\{ y - 3 z = - 11 }\\{ - 2 x - 6 y + 5 z = - 1 }\end{array} \right.$$

Solve for x, y, z

$$x=-181$$

$$y=88$$

$$z=33$$

Short Steps Using Substitution

Solve x+2y=-5 for x.

$$x=-2y-5$$

Substitute -2y-5 for x in the equation -2x-6y+5z=-1.

$$-2\left(-2y-5\right)-6y+5z=-1$$

Solve the second equation for y and the third equation for z.

$$y=3z-11 z=\frac{2}{5}y-\frac{11}{5}$$

Substitute 3z-11 for y in the equation z=\frac{2}{5}y-\frac{11}{5}.

$$z=\frac{2}{5}\left(3z-11\right)-\frac{11}{5}$$

Solve z=\frac{2}{5}\left(3z-11\right)-\frac{11}{5} for z.

$$z=33$$

Substitute 33 for z in the equation y=3z-11.

$$y=3\times 33-11$$

Calculate y from y=3\times 33-11.

$$y=88$$

Substitute 88 for y in the equation x=-2y-5.

$$x=-2\times 88-5$$

Calculate x from x=-2\times 88-5.

$$x=-181$$

The system is now solved.

$$x=-181 y=88 z=33$$