Solve {l}{x+y=-1}{x-y+z=7}{2x-y-z=0}

$$\left\{ \begin{array} { l } { x + y = - 1 } \\ { x - y + z = 7 } \\ { 2 x - y - z = 0 } \end{array} \right.$$

Solve for x, y, z

$$x=1$$

$$y=-2$$

$$z=4$$

Short Steps Using Substitution

Solve x+y=-1 for x.

$$x=-y-1$$

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

$$-y-1-y+z=7 2\left(-y-1\right)-y-z=0$$

Solve these equations for y and z respectively.

$$y=-4+\frac{1}{2}z z=-3y-2$$

Substitute -4+\frac{1}{2}z for y in the equation z=-3y-2.

$$z=-3\left(-4+\frac{1}{2}z\right)-2$$

Solve z=-3\left(-4+\frac{1}{2}z\right)-2 for z.

$$z=4$$

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

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

Calculate y from y=-4+\frac{1}{2}\times 4.

$$y=-2$$

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

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

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

$$x=1$$

The system is now solved.

$$x=1 y=-2 z=4$$