Solve {l}{x+y+z=-5}{3y+4z=-11}{-3y+3z=18}

$$\left. \begin{array}{l}{ x + y + z = - 5 }\\{ 3 y + 4 z = - 11 }\\{ - 3 y + 3 z = 18 }\end{array} \right.$$

Solve for x, y, z

$$x=-1$$

$$y=-5$$

$$z=1$$

Short Steps Using Substitution

Solve x+y+z=-5 for x.

$$x=-y-z-5$$

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

$$y=-\frac{4}{3}z-\frac{11}{3} z=6+y$$

Substitute -\frac{4}{3}z-\frac{11}{3} for y in the equation z=6+y.

$$z=6-\frac{4}{3}z-\frac{11}{3}$$

Solve z=6-\frac{4}{3}z-\frac{11}{3} for z.

$$z=1$$

Substitute 1 for z in the equation y=-\frac{4}{3}z-\frac{11}{3}.

$$y=-\frac{4}{3}-\frac{11}{3}$$

Calculate y from y=-\frac{4}{3}-\frac{11}{3}.

$$y=-5$$

Substitute -5 for y and 1 for z in the equation x=-y-z-5.

$$x=-\left(-5\right)-1-5$$

Calculate x from x=-\left(-5\right)-1-5.

$$x=-1$$

The system is now solved.

$$x=-1 y=-5 z=1$$