Question

The value of expression $mx-ny$ is $3$ when $x=5$ and $y=6$ . And its value is $8$ when $x=6$ and $y=5$ . Find the value of $m$ and $n$.

• A. $m=3;n=2$
• B. $m=2;n=3$
• C. $m=1;n=4$
• D. $m=1;n=8$

Answer 1

The correct option is A $m=3;n=2$

Given, $mx-ny=3$ when $x=5;y=6$
$=>5m-6n=3$ --- (1)
Also, $mx-ny=8$ when $x=6;y=5$
$=>6m-5n=8$ --- (1)

Multiplying equation $\left(1\right)$ with $5$ we get, $25m-30n=15$ ----- equation $\left(3\right)$

Multiplying equation $\left(2\right)$ with $6$ we get, $36m-30n=48$ ----- equation $\left(4\right)$

Subtracting equation $\left(3\right)$

from $\left(4\right)$, we get $11m=33=>m=3$

Substituting
$m=3$ in the equation $\left(1\right)$, we get $5\left(3\right)-6n=3=>n=2$