Solve {l}{4x+6y+z=-52}{x+5y+z=-26}{8x+4y+z=-80}

$$\left\{ \begin{array} { l } { 4 x + 6 y + z = - 52 } \\ { x + 5 y + z = - 26 } \\ { 8 x + 4 y + z = - 80 } \end{array} \right.$$

Solve for x, y, z

$$x=-8$$

$$y=-2$$

$$z=-8$$

Short Steps Using Substitution

Solve 4x+6y+z=-52 for z.

$$z=-52-4x-6y$$

Substitute -52-4x-6y for z in the second and third equation.

$$x+5y-52-4x-6y=-26 8x+4y-52-4x-6y=-80$$

Solve these equations for y and x respectively.

$$y=-3x-26 x=-7+\frac{1}{2}y$$

Substitute -3x-26 for y in the equation x=-7+\frac{1}{2}y.

$$x=-7+\frac{1}{2}\left(-3x-26\right)$$

Solve x=-7+\frac{1}{2}\left(-3x-26\right) for x.

$$x=-8$$

Substitute -8 for x in the equation y=-3x-26.

$$y=-3\left(-8\right)-26$$

Calculate y from y=-3\left(-8\right)-26.

$$y=-2$$

Substitute -2 for y and -8 for x in the equation z=-52-4x-6y.

$$z=-52-4\left(-8\right)-6\left(-2\right)$$

Calculate z from z=-52-4\left(-8\right)-6\left(-2\right).

$$z=-8$$

The system is now solved.

$$x=-8 y=-2 z=-8$$