Solve {l}{10c+10l=19}{20c+20p=37}{20l+20p=39}

$$\left\{ \begin{array} { l } { 10 c + 10 l = 19 } \\ { 20 c + 20 p = 37 } \\ { 20 l + 20 p = 39 } \end{array} \right.$$

Solve for c, l, p

$$c=\frac{9}{10}=0.9$$

$$l=1$$

$$p=\frac{19}{20}=0.95$$

Short Steps Using Substitution

Solve 10c+10l=19 for c.

$$c=-l+\frac{19}{10}$$

Substitute -l+\frac{19}{10} for c in the equation 20c+20p=37.

$$20\left(-l+\frac{19}{10}\right)+20p=37$$

Solve the second equation for l and the third equation for p.

$$l=\frac{1}{20}+p p=-l+\frac{39}{20}$$

Substitute \frac{1}{20}+p for l in the equation p=-l+\frac{39}{20}.

$$p=-\left(\frac{1}{20}+p\right)+\frac{39}{20}$$

Solve p=-\left(\frac{1}{20}+p\right)+\frac{39}{20} for p.

$$p=\frac{19}{20}$$

Substitute \frac{19}{20} for p in the equation l=\frac{1}{20}+p.

$$l=\frac{1}{20}+\frac{19}{20}$$

Calculate l from l=\frac{1}{20}+\frac{19}{20}.

$$l=1$$

Substitute 1 for l in the equation c=-l+\frac{19}{10}.

$$c=-1+\frac{19}{10}$$

Calculate c from c=-1+\frac{19}{10}.

$$c=\frac{9}{10}$$

The system is now solved.

$$c=\frac{9}{10} l=1 p=\frac{19}{20}$$