Question

Let $m$ be a positive integer and let the lines $13x+11y=700$ and $y=mx-1$ intersect in a point whose co-ordinates are integers. Then $m$ equals

• A. $7$
• B. $6$
• C. $5$
• D. $4$

Answer 1

Answer: (B)

$6$

Given equations
$13x+11y=700$ and $y=mx-1$

On solving, we get $x=\frac{711}{13+11m},y=\frac{700m-13}{13+11m}$
Since, $x$ and $y$ are integers, we will check by keeping the value of $m$ from each option.
Option A, $m=7$ does not give integer values of $x$ and $y$
Option B, $m=6$ only gives $x=9,y=53$
Similarly, option C and option D does not give integer value of $x,y$