Question

Solve in positive integers: $5x+2y=53$

• A. $x=1$, $y=24$
• B. $x=9$, $y=15$
• C. $x=3$, $y=1$
• D. $x=11$, $y=7$

Answer 1

The correct option is A $x=1$, $y=24$

$5x+2y=53$.
$y=\frac{53-5x}{2}$
Thus
$53-5x$ has to be a multiple of 2 for integral solutions. Hence x is of the form $2n+1$ where $nϵN$
Let $x=1$, we get $2y=48$ or $y=24$.
Hence $(1,24)$ is an integral solution of the above linear equation
Let $x=3$ then $y=19$
$x=5$ then $y=14$
$x=7$ then $y=9$
$x=9$ then $y=4$.
Hence the positive integral solutions of the above equation are
$(1,24),(3,19),(5,14),(7,9),(9,4)$