Question 4.

We have $2x + 5y = 99$ or $x = \frac{99 - 5y}{2}$

Now $x \ge y \ge -20$ ;  

So $\frac{99 - 5y}{2} \ge y$ ;  

$99 \ge 7y$ or $y \le \approx 14$

So $-20 \le y \le 14$.  

Now for this range of $y$, we have to find all the integral values of $x$.

As the coefficient of $x$ is $2$,

then $(99 - 5y)$ must be even, which will happen when $y$ is odd.  

However, there are only $17$ odd values of $y$ between $-20$ and $14$.

Hence the number of possible values is $17$.