Question 1024618
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System of Two Linear Equation : if man has $315 in ten and five dollar bills, how many of each does he have if he has 42 bills in all?
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 f +   t =  42,   (1)     (f = # of 5-dollar bills)
5f + 10t = 315.   (2)     (t = # of 10-dollar bills)

Express f = 42-t from (1) and substitute it into (2). You will get a single equation for t

5*(42-t) + 10t = 315.

Simplify and solve it:

210 - 5t + 10t = 315,

5t = 315 - 210,

5t = 105,

t = {{{105/5}}} = 21.

Thus there are 21 of 10-dollar bills.
Then the number of 5-dollar bills is 42-21 = 21.

Check: 5*21 + 10*21 = 105 + 210 = 315.   OK.
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