Solve {l}{2x-5=13}{2y+z=-18}{x-y-z=-28}

$$\left. \begin{array} { l } { 2 x - 5 = 13 } \\ { 2 y + z = - 18 } \\ { x - y - z = - 28 } \end{array} \right.$$

Solve for x, y, z

$$x=9$$

$$y=-55$$

$$z=92$$

Short Steps Using Substitution

Reorder the equations.

$$2y+z=-18 2x-5=13 x-y-z=-28$$

Solve 2y+z=-18 for z.

$$z=-18-2y$$

Substitute -18-2y for z in the equation x-y-z=-28.

$$x-y-\left(-18-2y\right)=-28$$

Solve the second equation for x and the third equation for y.

$$x=9 y=-x-46$$

Substitute 9 for x in the equation y=-x-46.

$$y=-9-46$$

Calculate y from y=-9-46.

$$y=-55$$

Substitute -55 for y in the equation z=-18-2y.

$$z=-18-2\left(-55\right)$$

Calculate z from z=-18-2\left(-55\right).

$$z=92$$

The system is now solved.

$$x=9 y=-55 z=92$$