Solve {l}{2x+y=-4}{-2y+4z=0}{3x-2z=-11}

$$\left\{ \begin{array}{l}{ 2 x + y = - 4 }\\{ - 2 y + 4 z = 0 }\\{ 3 x - 2 z = - 11 }\end{array} \right.$$

Solve for x, y, z

$$x=-3$$

$$y=2$$

$$z=1$$

Short Steps Using Substitution

Solve 2x+y=-4 for y.

$$y=-4-2x$$

Substitute -4-2x for y in the equation -2y+4z=0.

$$-2\left(-4-2x\right)+4z=0$$

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

$$x=-2-z z=\frac{3}{2}x+\frac{11}{2}$$

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

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

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

$$z=1$$

Substitute 1 for z in the equation x=-2-z.

$$x=-2-1$$

Calculate x from x=-2-1.

$$x=-3$$

Substitute -3 for x in the equation y=-4-2x.

$$y=-4-2\left(-3\right)$$

Calculate y from y=-4-2\left(-3\right).

$$y=2$$

The system is now solved.

$$x=-3 y=2 z=1$$