SOLUTION: A jar contains 70 coins, all of which are nickels and dimes. The total value of the coins in the jar is $5.70. How many nickels / dimes are in the jar?

Let n = # of nickels, d = # of dimes.

Then you have two equations in two unknowns

 n +   d =  70,   (1)
5n + 10d = 570.   (2)

To solve it, multiply equation (1) by 5 (both sides and all terms). Then distract it from the equation (2). You will get 

10d - 5d = 570 - 5*70,   or

5d = 570 - 350 = 220.

Hence, d =  = 44.

Thus there are 44 dimes in jar. 
Hence, the number of nickels is 70 - 44 = 26.

Check. 5*26 + 10*44 = 570.