The Equation 3x+11y = K Where K Is A 2 Digit Number Has Exactly Three Solutions In Which Both X And Y Are Positive Integers.

Question:

The equation 3x+11y=k where k is a 2 digit number has exactly three solutions in which both x and y are positive integers.
Which of the following is not a value of x? 5,17,19,25

 Answer:

In equation 3x+11y = k, x increases by 11 and y decreases by 3 as k is constant.

Now take the value of x= 5 and put y =1 we get k= 26(true) Next value of x = 5 + 11 = 16, k = 59(true).

Next value of x = 27, k = 92(true)

So solution set = {5, 16, 27}

Similarly check for x = 17.

For x = 19, we have k = 68 (true),

Next x = 30 then k = 108(false)

Even you take x = 19 - 11 = 8, k = 35 (true) but on x = 30 is false which is the third possible value of a solution set. and
 
At last x = 25, k = 86 (true)

Next value of x = 3, 14 having k = 20, 53 respectively.

So solution set {3, 14, 25}.