Question

Find the general solution in positive integers: $8x-21y=33$

• A. $x=2p-7$ and $y=8p-25$
• B. $x=p-9$ and $y=5-6p$
• C. $x=21p-9$ and $y=8p-5$
• D. $x=5p-3$ and $y=p+5$

Answer 1

The correct option is C $x=21p-9$ and $y=8p-5$

$8x-21y=33$ or $x=\frac{33+21y}{8}$.
Hence
$33+21y$ have to be a multiple of 8.
Let $y=3$ then $x=12$.
Similarly $y=11$ then $x=33$
Hence it follows an A.P
$x=12,33,\mathrm{45...}$
$y=3,11,\mathrm{19...}$.
Therefore
$x=12+(p-1)21=21p-21+12=21p-9$.
$y=3+(p-1)8=8p-8+3=8p-5$