Solve {l}{4=-8x+4y-2z}{0=-12x+2y}{-2/3=-12x}

$$\left. \begin{array} { l } { 4 = - 8 x + 4 y - 2 z } \\ { 0 = - 12 x + 2 y } \\ { - \frac { 2 } { 3 } = - 12 x } \end{array} \right.$$

Solve for x, y, z

$$x=\frac{1}{18}\approx 0.055555556$$

$$y=\frac{1}{3}\approx 0.333333333$$

$$z = -\frac{14}{9} = -1\frac{5}{9} \approx -1.555555556$$

Solution Steps

Consider the third equation. Divide both sides by -12.

$$\frac{-\frac{2}{3}}{-12}=x$$

Express \frac{-\frac{2}{3}}{-12} as a single fraction.

$$\frac{-2}{3\left(-12\right)}=x$$

Multiply 3 and -12 to get -36.

$$\frac{-2}{-36}=x$$

Reduce the fraction \frac{-2}{-36} to lowest terms by extracting and canceling out -2.

$$\frac{1}{18}=x$$

Swap sides so that all variable terms are on the left hand side.

$$x=\frac{1}{18}$$

Consider the second equation. Insert the known values of variables into the equation.

$$0=-12\times \frac{1}{18}+2y$$

Multiply -12 and \frac{1}{18} to get -\frac{2}{3}.

$$0=-\frac{2}{3}+2y$$

Swap sides so that all variable terms are on the left hand side.

$$-\frac{2}{3}+2y=0$$

Add \frac{2}{3} to both sides. Anything plus zero gives itself.

$$2y=\frac{2}{3}$$

Divide both sides by 2.

$$y=\frac{\frac{2}{3}}{2}$$

Express \frac{\frac{2}{3}}{2} as a single fraction.

$$y=\frac{2}{3\times 2}$$

Cancel out 2 in both numerator and denominator.

$$y=\frac{1}{3}$$

Consider the first equation. Insert the known values of variables into the equation.

$$4=-8\times \frac{1}{18}+4\times \frac{1}{3}-2z$$

Multiply -8 and \frac{1}{18} to get -\frac{4}{9}.

$$4=-\frac{4}{9}+4\times \frac{1}{3}-2z$$

Multiply 4 and \frac{1}{3} to get \frac{4}{3}.

$$4=-\frac{4}{9}+\frac{4}{3}-2z$$

Add -\frac{4}{9} and \frac{4}{3} to get \frac{8}{9}.

$$4=\frac{8}{9}-2z$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{8}{9}-2z=4$$

Subtract \frac{8}{9} from both sides.

$$-2z=4-\frac{8}{9}$$

Subtract \frac{8}{9} from 4 to get \frac{28}{9}.

$$-2z=\frac{28}{9}$$

Divide both sides by -2.

$$z=\frac{\frac{28}{9}}{-2}$$

Express \frac{\frac{28}{9}}{-2} as a single fraction.

$$z=\frac{28}{9\left(-2\right)}$$

Multiply 9 and -2 to get -18.

$$z=\frac{28}{-18}$$

Reduce the fraction \frac{28}{-18} to lowest terms by extracting and canceling out 2.

$$z=-\frac{14}{9}$$

The system is now solved.

$$x=\frac{1}{18} y=\frac{1}{3} z=-\frac{14}{9}$$