Question

The system of equations 2x – ay = 4; 5x – ky = 5 is inconsistent. If k and a are natural numbers, then the minimum possible value of (a + k) is equal to

• A. 7
• B. 14
• C. 5
• D. 3

Answer 1

The correct option is A 7

Given: 2x – ay = 4 and 5x – ky = 5
Now, the system of equations is inconsistent.

$\frac{2}{5}=\frac{-a}{-k}a=\frac{2k}{5}a+k=\frac{2k}{5}+k=\frac{7k}{5}$

Now, if a and k are natural numbers, then their sum is also a natural number.
Thus, for k = 5, a + k = 7, which is the minimum possible value of a + k.
Hence, the correct answer is option (1).