Solve {l}{6s=30}{2m+s=20}{4B+m=17}

$$\left\{ \begin{array} { l } { 6 s = 30 } \\ { 2 m + s = 20 } \\ { 4 B + m = 17 } \end{array} \right.$$

Solve for s, m, B

$$s=5$$

$$m = \frac{15}{2} = 7\frac{1}{2} = 7.5$$

$$B = \frac{19}{8} = 2\frac{3}{8} = 2.375$$

Solution Steps

Consider the first equation. Divide both sides by 6.

$$s=\frac{30}{6}$$

Divide 30 by 6 to get 5.

$$s=5$$

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

$$2m+5=20$$

Subtract 5 from both sides.

$$2m=20-5$$

Subtract 5 from 20 to get 15.

$$2m=15$$

Divide both sides by 2.

$$m=\frac{15}{2}$$

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

$$4B+\frac{15}{2}=17$$

Subtract \frac{15}{2} from both sides.

$$4B=17-\frac{15}{2}$$

Subtract \frac{15}{2} from 17 to get \frac{19}{2}.

$$4B=\frac{19}{2}$$

Divide both sides by 4.

$$B=\frac{\frac{19}{2}}{4}$$

Express \frac{\frac{19}{2}}{4} as a single fraction.

$$B=\frac{19}{2\times 4}$$

Multiply 2 and 4 to get 8.

$$B=\frac{19}{8}$$

The system is now solved.

$$s=5 m=\frac{15}{2} B=\frac{19}{8}$$