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Try small integer values of $ y $ and solve for $ x $:
Question: What is the smallest four-digit number that is divisible by $ 13 $ and leaves a remainder of $ 5 $ when divided by $ 7 $?
Solution: We seek the smallest four-digit number $ N $ such that:
So $ k = 7m + 2 $, and $ N = 13k = 13(7m + 2) = 91m + 26 $
We want the smallest four-digit $ N $, so:
So the smallest integer $ m = 11 $, then:
First, divide $ 98765 $ by $ 12345 $:
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