Solve {l}{x+x+x=30}{y+y+x=20}{2z+2z+y=13}

$$\left\{ \begin{array} { l } { x + x + x = 30 } \\ { y + y + x = 20 } \\ { 2 z + 2 z + y = 13 } \end{array} \right.$$

Solve for x, y, z

$$x=10$$

$$y=5$$

$$z=2$$

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.

$$y+y+10=20$$

Combine y and y to get 2y.

$$2y+10=20$$

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.

$$2z+2z+5=13$$

Combine 2z and 2z to get 4z.

$$4z+5=13$$

Subtract 5 from both sides.

$$4z=13-5$$

Subtract 5 from 13 to get 8.

$$4z=8$$

Divide both sides by 4.

$$z=\frac{8}{4}$$

Divide 8 by 4 to get 2.

$$z=2$$

The system is now solved.

$$x=10 y=5 z=2$$