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

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

Solve for x, y, z

$$x=-3$$

$$y=2$$

$$z=2$$

Short Steps Using Substitution

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

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

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

$$-y+z-3-y+4z=3 -y+z-3+5y-5z=-3$$

Solve these equations for y and z respectively.

$$y=\frac{5}{2}z-3 z=y$$

Substitute \frac{5}{2}z-3 for y in the equation z=y.

$$z=\frac{5}{2}z-3$$

Solve z=\frac{5}{2}z-3 for z.

$$z=2$$

Substitute 2 for z in the equation y=\frac{5}{2}z-3.

$$y=\frac{5}{2}\times 2-3$$

Calculate y from y=\frac{5}{2}\times 2-3.

$$y=2$$

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

$$x=-2+2-3$$

Calculate x from x=-2+2-3.

$$x=-3$$

The system is now solved.

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