Solve {l}{x+x+x=30}{x+y+y=18}{y-2z=2}{a=z+x+y}{text{Solvefor}btext{where}}{b=a}

$$\left. \begin{array} { l } { x + x + x = 30 }\\ { x + y + y = 18 }\\ { y - 2 z = 2 }\\ { a = z + x + y }\\ { \text{Solve for } b \text{ where} } \\ { b = a } \end{array} \right.$$

Solve for x, y, z, a, b

$$b=15$$

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.

$$10+y+y=18$$

Combine y and y to get 2y.

$$10+2y=18$$

Subtract 10 from both sides.

$$2y=18-10$$

Subtract 10 from 18 to get 8.

$$2y=8$$

Divide both sides by 2.

$$y=\frac{8}{2}$$

Divide 8 by 2 to get 4.

$$y=4$$

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

$$4-2z=2$$

Subtract 4 from both sides.

$$-2z=2-4$$

Subtract 4 from 2 to get -2.

$$-2z=-2$$

Divide both sides by -2.

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

Divide -2 by -2 to get 1.

$$z=1$$

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

$$a=1+10+4$$

Add 1 and 10 to get 11.

$$a=11+4$$

Add 11 and 4 to get 15.

$$a=15$$

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

$$b=15$$

The system is now solved.

$$x=10 y=4 z=1 a=15 b=15$$