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

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

Solve for x, y, z

$$x=5$$

$$y=10$$

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

Solution Steps

Consider the first equation. Combine 2x and 2x to get 4x.

$$4x+2x=30$$

Combine 4x and 2x to get 6x.

$$6x=30$$

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.

$$y+y+2\times 5=30$$

Combine y and y to get 2y.

$$2y+2\times 5=30$$

Multiply 2 and 5 to get 10.

$$2y+10=30$$

Subtract 10 from both sides.

$$2y=30-10$$

Subtract 10 from 30 to get 20.

$$2y=20$$

Divide both sides by 2.

$$y=\frac{20}{2}$$

Divide 20 by 2 to get 10.

$$y=10$$

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

$$2z+2z+10=13$$

Combine 2z and 2z to get 4z.

$$4z+10=13$$

Subtract 10 from both sides.

$$4z=13-10$$

Subtract 10 from 13 to get 3.

$$4z=3$$

Divide both sides by 4.

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

The system is now solved.

$$x=5 y=10 z=\frac{3}{4}$$