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I have a bunch of nickels and quarters worth \$7.85 in my [pocket. How do I write a system of equation to solve and determine how many of each coin I have!!

5N + 25Q = 785

N + 5Q = 157
N = 157 - 5Q

Of course you cannot have a unique solution, since you don't have enough information to form a second equation.
But...
you said he has a bunch of nickels and quarters, so he has at least one of each

so let Q be a number form 1 to 25 to get different combinations

Q N ------ combination ----------- value
1 152 ---- 1 quarter + 152 nickels = \$7.85
2 147 -----2 quarters + 147 nickels = \$7.85
...
25 32 ----- 25 quarters + 32 nickels = \$7.85

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