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

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

Solve for M, B, C, a, b

$$b=16$$

Solution Steps

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

$$2M+M=3$$

Combine 2M and M to get 3M.

$$3M=3$$

Divide both sides by 3.

$$M=\frac{3}{3}$$

Divide 3 by 3 to get 1.

$$M=1$$

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

$$1+B+B=18$$

Combine B and B to get 2B.

$$1+2B=18$$

Subtract 1 from both sides.

$$2B=18-1$$

Subtract 1 from 18 to get 17.

$$2B=17$$

Divide both sides by 2.

$$B=\frac{17}{2}$$

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

$$\frac{17}{2}-C=2$$

Subtract \frac{17}{2} from both sides.

$$-C=2-\frac{17}{2}$$

Subtract \frac{17}{2} from 2 to get -\frac{13}{2}.

$$-C=-\frac{13}{2}$$

Divide both sides by -1.

$$C=\frac{-\frac{13}{2}}{-1}$$

Express \frac{-\frac{13}{2}}{-1} as a single fraction.

$$C=\frac{-13}{2\left(-1\right)}$$

Multiply 2 and -1 to get -2.

$$C=\frac{-13}{-2}$$

Fraction \frac{-13}{-2} can be simplified to \frac{13}{2} by removing the negative sign from both the numerator and the denominator.

$$C=\frac{13}{2}$$

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

$$a=\frac{13}{2}+1+\frac{17}{2}$$

Add \frac{13}{2} and 1 to get \frac{15}{2}.

$$a=\frac{15}{2}+\frac{17}{2}$$

Add \frac{15}{2} and \frac{17}{2} to get 16.

$$a=16$$

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

$$b=16$$

The system is now solved.

$$M=1 B=\frac{17}{2} C=\frac{13}{2} a=16 b=16$$