Solve 2x+y-z+2=0,quad3x-z=5,4y+3z=9

$$2 x + y - z + 2 = 0 , \quad 3 x - z = 5,4 y + 3 z = 9$$

Solve for x, y, z

$$x=4$$

$$y=-3$$

$$z=7$$

Short Steps Using Substitution

Solve 2x+y-z+2=0 for y.

$$y=-2x+z-2$$

Substitute -2x+z-2 for y in the equation 4y+3z=9.

$$4\left(-2x+z-2\right)+3z=9$$

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

$$x=\frac{5}{3}+\frac{1}{3}z z=\frac{8}{7}x+\frac{17}{7}$$

Substitute \frac{5}{3}+\frac{1}{3}z for x in the equation z=\frac{8}{7}x+\frac{17}{7}.

$$z=\frac{8}{7}\left(\frac{5}{3}+\frac{1}{3}z\right)+\frac{17}{7}$$

Solve z=\frac{8}{7}\left(\frac{5}{3}+\frac{1}{3}z\right)+\frac{17}{7} for z.

$$z=7$$

Substitute 7 for z in the equation x=\frac{5}{3}+\frac{1}{3}z.

$$x=\frac{5}{3}+\frac{1}{3}\times 7$$

Calculate x from x=\frac{5}{3}+\frac{1}{3}\times 7.

$$x=4$$

Substitute 4 for x and 7 for z in the equation y=-2x+z-2.

$$y=-2\times 4+7-2$$

Calculate y from y=-2\times 4+7-2.

$$y=-3$$

The system is now solved.

$$x=4 y=-3 z=7$$