Solve {l}{2x+y-3z=-6}{4x+y+z=10}{-3x+y+2z=-1}

$$\left\{ \begin{array} { l } { 2 x + y - 3 z = - 6 } \\ { 4 x + y + z = 10 } \\ { - 3 x + y + 2 z = - 1 } \end{array} \right.$$

Solve for x, y, z

$$x=2$$

$$y=-1$$

$$z=3$$

Short Steps Using Substitution

Solve 2x+y-3z=-6 for y.

$$y=-2x+3z-6$$

Substitute -2x+3z-6 for y in the second and third equation.

$$4x-2x+3z-6+z=10 -3x-2x+3z-6+2z=-1$$

Solve these equations for x and z respectively.

$$x=8-2z z=1+x$$

Substitute 8-2z for x in the equation z=1+x.

$$z=1+8-2z$$

Solve z=1+8-2z for z.

$$z=3$$

Substitute 3 for z in the equation x=8-2z.

$$x=8-2\times 3$$

Calculate x from x=8-2\times 3.

$$x=2$$

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

$$y=-2\times 2+3\times 3-6$$

Calculate y from y=-2\times 2+3\times 3-6.

$$y=-1$$

The system is now solved.

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