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AlgebraMediumSmallest positive integer solution of a two-variable equation

Algebra practice question

In the equation 3x − 2y = 7, both x and y are positive integers. What is the smallest possible value of x?

Answer: 3

x = 1 gives y = −2 and x = 2 gives y = −1/2, neither allowed; x = 3 gives y = 1.

Common wrong answers

If you answered 1
1 gives y = −2, which is not positive.
If you answered 2
2 gives y = −1/2, not an integer.
If you answered 7
7 solves 3x = 7 + 2y with y = 7, but smaller x work.

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