Solve {l}{2x+4y+3z=6}{x+2z=-1}{-2y+z=-5}

$$\left\{ \begin{array}{l}{ 2 x + 4 y + 3 z = 6 }\\{ x + 2 z = - 1 }\\{ - 2 y + z = - 5 }\end{array} \right.$$

Solve for x, y, z

$$x=3$$

$$y = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

$$z=-2$$

Short Steps Using Substitution

Reorder the equations.

$$x+2z=-1 2x+4y+3z=6 -2y+z=-5$$

Solve x+2z=-1 for x.

$$x=-2z-1$$

Substitute -2z-1 for x in the equation 2x+4y+3z=6.

$$2\left(-2z-1\right)+4y+3z=6$$

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

$$y=\frac{1}{4}z+2 z=2y-5$$

Substitute \frac{1}{4}z+2 for y in the equation z=2y-5.

$$z=2\left(\frac{1}{4}z+2\right)-5$$

Solve z=2\left(\frac{1}{4}z+2\right)-5 for z.

$$z=-2$$

Substitute -2 for z in the equation y=\frac{1}{4}z+2.

$$y=\frac{1}{4}\left(-2\right)+2$$

Calculate y from y=\frac{1}{4}\left(-2\right)+2.

$$y=\frac{3}{2}$$

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

$$x=-2\left(-2\right)-1$$

Calculate x from x=-2\left(-2\right)-1.

$$x=3$$

The system is now solved.

$$x=3 y=\frac{3}{2} z=-2$$