Solve {l}{2x-y+8z=13,3x+4y+5z=18}{5x-2y+7z=20}

$$\left. \begin{array} { l } { 2 x - y + 8 z = 13,3 x + 4 y + 5 z = 18 } \\ { 5 x - 2 y + 7 z = 20 } \end{array} \right.$$

Solve for x, y, z

$$x=3$$

$$y=1$$

$$z=1$$

Short Steps Using Substitution

Solve 2x-y+8z=13 for y.

$$y=2x+8z-13$$

Substitute 2x+8z-13 for y in the second and third equation.

$$3x+4\left(2x+8z-13\right)+5z=18 5x-2\left(2x+8z-13\right)+7z=20$$

Solve these equations for x and z respectively.

$$x=-\frac{37}{11}z+\frac{70}{11} z=\frac{1}{9}x+\frac{2}{3}$$

Substitute -\frac{37}{11}z+\frac{70}{11} for x in the equation z=\frac{1}{9}x+\frac{2}{3}.

$$z=\frac{1}{9}\left(-\frac{37}{11}z+\frac{70}{11}\right)+\frac{2}{3}$$

Solve z=\frac{1}{9}\left(-\frac{37}{11}z+\frac{70}{11}\right)+\frac{2}{3} for z.

$$z=1$$

Substitute 1 for z in the equation x=-\frac{37}{11}z+\frac{70}{11}.

$$x=-\frac{37}{11}+\frac{70}{11}$$

Calculate x from x=-\frac{37}{11}+\frac{70}{11}.

$$x=3$$

Substitute 3 for x and 1 for z in the equation y=2x+8z-13.

$$y=2\times 3+8\times 1-13$$

Calculate y from y=2\times 3+8\times 1-13.

$$y=1$$

The system is now solved.

$$x=3 y=1 z=1$$