Solve {l}{6x=30}{2y+2x=20}{6z+y=1}

$$\left\{ \begin{array} { l } { 6 x = 30 } \\ { 2 y + 2 x = 20 } \\ { 6 z + y = 1 } \end{array} \right.$$

Solve for x, y, z

$$x=5$$

$$y=5$$

$$z=-\frac{2}{3}\approx -0.666666667$$

Solution Steps

Consider the first equation. Divide both sides by 6.

$$x=\frac{30}{6}$$

Divide 30 by 6 to get 5.

$$x=5$$

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

$$2y+2\times 5=20$$

Multiply 2 and 5 to get 10.

$$2y+10=20$$

Subtract 10 from both sides.

$$2y=20-10$$

Subtract 10 from 20 to get 10.

$$2y=10$$

Divide both sides by 2.

$$y=\frac{10}{2}$$

Divide 10 by 2 to get 5.

$$y=5$$

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

$$6z+5=1$$

Subtract 5 from both sides.

$$6z=1-5$$

Subtract 5 from 1 to get -4.

$$6z=-4$$

Divide both sides by 6.

$$z=\frac{-4}{6}$$

Reduce the fraction \frac{-4}{6} to lowest terms by extracting and canceling out 2.

$$z=-\frac{2}{3}$$

The system is now solved.

$$x=5 y=5 z=-\frac{2}{3}$$