Solve {l}{x+y-z=-6}{-x+y+3z=-4}{3x-5y-3z=14}

$$\left. \begin{array}{l}{ x + y - z = - 6 }\\{ - x + y + 3 z = - 4 }\\{ 3 x - 5 y - 3 z = 14 }\end{array} \right.$$

Solve for x, y, z

$$x=-3$$

$$y=-4$$

$$z=-1$$

Short Steps Using Substitution

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

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

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

$$-\left(-y+z-6\right)+y+3z=-4 3\left(-y+z-6\right)-5y-3z=14$$

Solve these equations for z and y respectively.

$$z=-5-y y=-4$$

Substitute -4 for y in the equation z=-5-y.

$$z=-5-\left(-4\right)$$

Calculate z from z=-5-\left(-4\right).

$$z=-1$$

Substitute -1 for z and -4 for y in the equation x=-y+z-6.

$$x=-\left(-4\right)-1-6$$

Calculate x from x=-\left(-4\right)-1-6.

$$x=-3$$

The system is now solved.

$$x=-3 y=-4 z=-1$$