Question

Find the limits within which $c$ must lie in order that the equation $19x+14y=c$ may have six solutions, zero solutions being excluded.

Answer 1

The greatest value of $c=(n+1)ab-a-b=7\times 19\times 14-19-14=1829$

The least value of $c=(n-1)ab+a+b=5\times 19\times 14+19+14=1363$

Here, $n=$ no of solutions

$a$ and $b$ are coefficents of $x$ and $y$ respectively.

Hence, the value of $c$ lies between $1829$ and $1363$.