Solve {c}{-10x+y-5z=-7}{2x+y+5z=1}{3x-3y-5z=8}

$$\left. \begin{array} { c } { - 10 x + y - 5 z = - 7 } \\ { 2 x + y + 5 z = 1 } \\ { 3 x - 3 y - 5 z = 8 } \end{array} \right.$$

Solve for x, y, z

$$x=-1$$

$$y=-7$$

$$z=2$$

Short Steps Using Substitution

Solve -10x+y-5z=-7 for y.

$$y=10x+5z-7$$

Substitute 10x+5z-7 for y in the second and third equation.

$$2x+10x+5z-7+5z=1 3x-3\left(10x+5z-7\right)-5z=8$$

Solve these equations for x and z respectively.

$$x=\frac{2}{3}-\frac{5}{6}z z=-\frac{27}{20}x+\frac{13}{20}$$

Substitute \frac{2}{3}-\frac{5}{6}z for x in the equation z=-\frac{27}{20}x+\frac{13}{20}.

$$z=-\frac{27}{20}\left(\frac{2}{3}-\frac{5}{6}z\right)+\frac{13}{20}$$

Solve z=-\frac{27}{20}\left(\frac{2}{3}-\frac{5}{6}z\right)+\frac{13}{20} for z.

$$z=2$$

Substitute 2 for z in the equation x=\frac{2}{3}-\frac{5}{6}z.

$$x=\frac{2}{3}-\frac{5}{6}\times 2$$

Calculate x from x=\frac{2}{3}-\frac{5}{6}\times 2.

$$x=-1$$

Substitute -1 for x and 2 for z in the equation y=10x+5z-7.

$$y=10\left(-1\right)+5\times 2-7$$

Calculate y from y=10\left(-1\right)+5\times 2-7.

$$y=-7$$

The system is now solved.

$$x=-1 y=-7 z=2$$