Solve {l}{x+y+2z=2}{x-3y+4z=2}{3x-y+6z=5}

$$\left. \begin{array} { l } { x + y + 2 z = 2 } \\ { x - 3 y + 4 z = 2 } \\ { 3 x - y + 6 z = 5 } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{3}{4}=0.75$$

$$y=\frac{1}{4}=0.25$$

$$z=\frac{1}{2}=0.5$$

Short Steps Using Substitution

Solve x+y+2z=2 for x.

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

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

$$-y-2z+2-3y+4z=2 3\left(-y-2z+2\right)-y+6z=5$$

Solve these equations for z and y respectively.

$$z=2y y=\frac{1}{4}$$

Substitute \frac{1}{4} for y in the equation z=2y.

$$z=2\times \frac{1}{4}$$

Calculate z from z=2\times \frac{1}{4}.

$$z=\frac{1}{2}$$

Substitute \frac{1}{2} for z and \frac{1}{4} for y in the equation x=-y-2z+2.

$$x=-\frac{1}{4}-2\times \frac{1}{2}+2$$

Calculate x from x=-\frac{1}{4}-2\times \frac{1}{2}+2.

$$x=\frac{3}{4}$$

The system is now solved.

$$x=\frac{3}{4} y=\frac{1}{4} z=\frac{1}{2}$$