Solve {l}{2x-1y=10}{1x-4y-120=60}{-1y+2z=-30}

$$\left. \begin{array} { l } { 2 x - 1 y = 10 } \\ { 1 x - 4 y - 120 = 60 } \\ { - 1 y + 2 z = - 30 } \end{array} \right.$$

Solve for x, y, z

$$x=-20$$

$$y=-50$$

$$z=-40$$

Short Steps Using Substitution

Solve 2x-y=10 for y.

$$y=-10+2x$$

Substitute -10+2x for y in the second and third equation.

$$1x-4\left(-10+2x\right)-120=60 -\left(-10+2x\right)+2z=-30$$

Solve these equations for x and z respectively.

$$x=-20 z=-20+x$$

Substitute -20 for x in the equation z=-20+x.

$$z=-20-20$$

Calculate z from z=-20-20.

$$z=-40$$

Substitute -20 for x in the equation y=-10+2x.

$$y=-10+2\left(-20\right)$$

Calculate y from y=-10+2\left(-20\right).

$$y=-50$$

The system is now solved.

$$x=-20 y=-50 z=-40$$