Solve {l}{x+x+x=30}{x+2y=20}{y+4z=0}

$$\left\{ \begin{array} { l } { x + x + x = 30 } \\ { x + 2 y = 20 } \\ { y + 4 z = 0 } \end{array} \right.$$

Solve for x, y, z

$$x=10$$

$$y=5$$

$$z = -\frac{5}{4} = -1\frac{1}{4} = -1.25$$

Solution Steps

Consider the first equation. Combine x and x to get 2x.

$$2x+x=30$$

Combine 2x and x to get 3x.

$$3x=30$$

Divide both sides by 3.

$$x=\frac{30}{3}$$

Divide 30 by 3 to get 10.

$$x=10$$

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

$$10+2y=20$$

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.

$$5+4z=0$$

Subtract 5 from both sides. Anything subtracted from zero gives its negation.

$$4z=-5$$

Divide both sides by 4.

$$z=-\frac{5}{4}$$

The system is now solved.

$$x=10 y=5 z=-\frac{5}{4}$$