Solve {l}{5x+2y-z=-7}{x-2y+2z=0}{3y+z=17}

$$\left\{ \begin{array} { l } { 5 x + 2 y - z = - 7 } \\ { x - 2 y + 2 z = 0 } \\ { 3 y + z = 17 } \end{array} \right\}$$

Solve for x, y, z

$$x=-2$$

$$y=4$$

$$z=5$$

Short Steps Using Substitution

Solve 5x+2y-z=-7 for z.

$$z=5x+2y+7$$

Substitute 5x+2y+7 for z in the second and third equation.

$$x-2y+2\left(5x+2y+7\right)=0 3y+5x+2y+7=17$$

Solve these equations for y and x respectively.

$$y=-\frac{11}{2}x-7 x=2-y$$

Substitute -\frac{11}{2}x-7 for y in the equation x=2-y.

$$x=2-\left(-\frac{11}{2}x-7\right)$$

Solve x=2-\left(-\frac{11}{2}x-7\right) for x.

$$x=-2$$

Substitute -2 for x in the equation y=-\frac{11}{2}x-7.

$$y=-\frac{11}{2}\left(-2\right)-7$$

Calculate y from y=-\frac{11}{2}\left(-2\right)-7.

$$y=4$$

Substitute 4 for y and -2 for x in the equation z=5x+2y+7.

$$z=5\left(-2\right)+2\times 4+7$$

Calculate z from z=5\left(-2\right)+2\times 4+7.

$$z=5$$

The system is now solved.

$$x=-2 y=4 z=5$$