Solve {c}{2x+2y-9z=16}{6x+7y-26z=62}{10x+18y-55z=156}

$$\left. \begin{array} { c } { 2 x + 2 y - 9 z = 16 } \\ { 6 x + 7 y - 26 z = 62 } \\ { 10 x + 18 y - 55 z = 156 } \end{array} \right.$$

Solve for x, y, z

$$x=5$$

$$y=12$$

$$z=2$$

Short Steps Using Substitution

Solve 2x+2y-9z=16 for x.

$$x=-y+\frac{9}{2}z+8$$

Substitute -y+\frac{9}{2}z+8 for x in the second and third equation.

$$6\left(-y+\frac{9}{2}z+8\right)+7y-26z=62 10\left(-y+\frac{9}{2}z+8\right)+18y-55z=156$$

Solve these equations for y and z respectively.

$$y=-z+14 z=-\frac{38}{5}+\frac{4}{5}y$$

Substitute -z+14 for y in the equation z=-\frac{38}{5}+\frac{4}{5}y.

$$z=-\frac{38}{5}+\frac{4}{5}\left(-z+14\right)$$

Solve z=-\frac{38}{5}+\frac{4}{5}\left(-z+14\right) for z.

$$z=2$$

Substitute 2 for z in the equation y=-z+14.

$$y=-2+14$$

Calculate y from y=-2+14.

$$y=12$$

Substitute 12 for y and 2 for z in the equation x=-y+\frac{9}{2}z+8.

$$x=-12+\frac{9}{2}\times 2+8$$

Calculate x from x=-12+\frac{9}{2}\times 2+8.

$$x=5$$

The system is now solved.

$$x=5 y=12 z=2$$