Solve {l}{-x+y+z=-1}{x-2y+z=7}{4x+2y-2z=-4}

$$\left. \begin{array}{l}{ - x + y + z = - 1 }\\{ x - 2 y + z = 7 }\\{ 4 x + 2 y - 2 z = - 4 }\end{array} \right.$$

Solve for x, y, z

$$x=1$$

$$y=-2$$

$$z=2$$

Short Steps Using Substitution

Solve -x+y+z=-1 for x.

$$x=y+z+1$$

Substitute y+z+1 for x in the second and third equation.

$$y+z+1-2y+z=7 4\left(y+z+1\right)+2y-2z=-4$$

Solve these equations for y and z respectively.

$$y=-6+2z z=-4-3y$$

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

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

Solve z=-4-3\left(-6+2z\right) for z.

$$z=2$$

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

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

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

$$y=-2$$

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

$$x=-2+2+1$$

Calculate x from x=-2+2+1.

$$x=1$$

The system is now solved.

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