Solve {l}{x+y+z=-10}{x-y+3z=-8}{4x+y+z=-25}

$$\left\{ \begin{array}{l}{ x + y + z = - 10 }\\{ x - y + 3 z = - 8 }\\{ 4 x + y + z = - 25 }\end{array} \right.$$

Solve for x, y, z

$$x=-5$$

$$y=-3$$

$$z=-2$$

Short Steps Using Substitution

Solve x+y+z=-10 for x.

$$x=-y-z-10$$

Substitute -y-z-10 for x in the second and third equation.

$$-y-z-10-y+3z=-8 4\left(-y-z-10\right)+y+z=-25$$

Solve these equations for y and z respectively.

$$y=-1+z z=-5-y$$

Substitute -1+z for y in the equation z=-5-y.

$$z=-5-\left(-1+z\right)$$

Solve z=-5-\left(-1+z\right) for z.

$$z=-2$$

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

$$y=-1-2$$

Calculate y from y=-1-2.

$$y=-3$$

Substitute -3 for y and -2 for z in the equation x=-y-z-10.

$$x=-\left(-3\right)-\left(-2\right)-10$$

Calculate x from x=-\left(-3\right)-\left(-2\right)-10.

$$x=-5$$

The system is now solved.

$$x=-5 y=-3 z=-2$$