Solve {l}{-11=-3/2+b}{9=81c+b}

$$\left\{ \begin{array} { l } { - 11 = - 3 / 2 + b } \\ { 9 = 81 c + b } \end{array} \right.$$

Solve for b, c

$$b = -\frac{19}{2} = -9\frac{1}{2} = -9.5$$

$$c=\frac{37}{162}\approx 0.228395062$$

Solution Steps

Consider the first equation. Swap sides so that all variable terms are on the left hand side.

$$-\frac{3}{2}+b=-11$$

Add \frac{3}{2} to both sides.

$$b=-11+\frac{3}{2}$$

Add -11 and \frac{3}{2} to get -\frac{19}{2}.

$$b=-\frac{19}{2}$$

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

$$9=81c-\frac{19}{2}$$

Swap sides so that all variable terms are on the left hand side.

$$81c-\frac{19}{2}=9$$

Add \frac{19}{2} to both sides.

$$81c=9+\frac{19}{2}$$

Add 9 and \frac{19}{2} to get \frac{37}{2}.

$$81c=\frac{37}{2}$$

Divide both sides by 81.

$$c=\frac{\frac{37}{2}}{81}$$

Express \frac{\frac{37}{2}}{81} as a single fraction.

$$c=\frac{37}{2\times 81}$$

Multiply 2 and 81 to get 162.

$$c=\frac{37}{162}$$

The system is now solved.

$$b=-\frac{19}{2} c=\frac{37}{162}$$