Notes here, and on pages 369-400 in book

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For any of these, you must (probably) create two equations and then solve by substitution or by addition (elimination).

For instance,

You have a bunch of quarters and dimes such that you have 14 total coins. The value of all of thes coins are $2.15. What are the number of each type of coin?

q + d =14

.25q + .10d=2.15

If you don't like dealing with decimals, multiply they second equation times 100.

25q + 10d = 215

Substituting in d=14-q gives 25q+10(14-q)=215. This eventually yields 5 quarters and 9 dimes which definitely adds up to 14 coins and will total to $1.25 + .90 = $2.15.