Solve {l}{m+m+m=30}{m+4B+4B=18}{4B-2C=2}{a=C+m+3B}{text{Solvefor}btext{where}}{b=a}

$$\left. \begin{array} { l } { m + m + m = 30 }\\ { m + 4 B + 4 B = 18 }\\ { 4 B - 2 C = 2 }\\ { a = C + m + 3 B }\\ { \text{Solve for } b \text{ where} } \\ { b = a } \end{array} \right.$$

Solve for m, B, C, a, b

$$b=14$$

Solution Steps

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

$$2m+m=30$$

Combine 2m and m to get 3m.

$$3m=30$$

Divide both sides by 3.

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

Divide 30 by 3 to get 10.

$$m=10$$

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

$$10+4B+4B=18$$

Combine 4B and 4B to get 8B.

$$10+8B=18$$

Subtract 10 from both sides.

$$8B=18-10$$

Subtract 10 from 18 to get 8.

$$8B=8$$

Divide both sides by 8.

$$B=\frac{8}{8}$$

Divide 8 by 8 to get 1.

$$B=1$$

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

$$4\times 1-2C=2$$

Multiply 4 and 1 to get 4.

$$4-2C=2$$

Subtract 4 from both sides.

$$-2C=2-4$$

Subtract 4 from 2 to get -2.

$$-2C=-2$$

Divide both sides by -2.

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

Divide -2 by -2 to get 1.

$$C=1$$

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

$$a=1+10+3\times 1$$

Add 1 and 10 to get 11.

$$a=11+3\times 1$$

Multiply 3 and 1 to get 3.

$$a=11+3$$

Add 11 and 3 to get 14.

$$a=14$$

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

$$b=14$$

The system is now solved.

$$m=10 B=1 C=1 a=14 b=14$$