Question

If x and y are two natural numbers such that x > 19 and y < 5, which number line represents the location of a point P= x/2+5y such that P has the least possible value?

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Answer 1

Answer:

The equation 2x+5y=7 is a Diophantine equation whose solution is:  

x=5n+1 and y=1−2n  where n are integers  

Obviously for there to be only one (unique) answer, x and y must be restricted to the natural numbers. (or n=0).

Clearly, x=1 and y=1 is a solution of the equation 2x+5y=7.  

It is clearly the only solution, since using any other natural numbers (which are positive integers) produces 2x+5y which is greater than 7.  

If we include all real numbers, the graph is a line, and any point on the line is a solution. It happens that the only point with positive integer coefficients is (1,1).

Step-by-step explanation: