Solve {l}{5/8+12c+E+11F=0}{1/8+c+F=0}{18c+4E+12F=11/2}

$$\left\{ \begin{array} { l } { \frac { 5 } { 8 } + 12 c + E + 11 F = 0 } \\ { \frac { 1 } { 8 } + c + F = 0 } \\ { 18 c + 4 E + 12 F = \frac { 11 } { 2 } } \end{array} \right.$$

Solve for c, E, F

$$c=2$$

$$E = -\frac{5}{4} = -1\frac{1}{4} = -1.25$$

$$F = -\frac{17}{8} = -2\frac{1}{8} = -2.125$$

Short Steps Using Substitution

Solve \frac{5}{8}+12c+E+11F=0 for E.

$$E=-\frac{5}{8}-12c-11F$$

Substitute -\frac{5}{8}-12c-11F for E in the equation 18c+4E+12F=\frac{11}{2}.

$$18c+4\left(-\frac{5}{8}-12c-11F\right)+12F=\frac{11}{2}$$

Solve the second equation for c and the third equation for F.

$$c=-\frac{1}{8}-F F=-\frac{1}{4}-\frac{15}{16}c$$

Substitute -\frac{1}{8}-F for c in the equation F=-\frac{1}{4}-\frac{15}{16}c.

$$F=-\frac{1}{4}-\frac{15}{16}\left(-\frac{1}{8}-F\right)$$

Solve F=-\frac{1}{4}-\frac{15}{16}\left(-\frac{1}{8}-F\right) for F.

$$F=-\frac{17}{8}$$

Substitute -\frac{17}{8} for F in the equation c=-\frac{1}{8}-F.

$$c=-\frac{1}{8}-\left(-\frac{17}{8}\right)$$

Calculate c from c=-\frac{1}{8}-\left(-\frac{17}{8}\right).

$$c=2$$

Substitute 2 for c and -\frac{17}{8} for F in the equation E=-\frac{5}{8}-12c-11F.

$$E=-\frac{5}{8}-12\times 2-11\left(-\frac{17}{8}\right)$$

Calculate E from E=-\frac{5}{8}-12\times 2-11\left(-\frac{17}{8}\right).

$$E=-\frac{5}{4}$$

The system is now solved.

$$c=2 E=-\frac{5}{4} F=-\frac{17}{8}$$