Question

The value of the expression $mx - ny = 3$ when $x = 5$& $y = 6$. And its value is $8$ when $x = 6$ & $y = 5$. Find the value of $m\& n$.
A: $m = 3,n = 2$
B: $m = 2,n = 3$
C: $m = 1,n = 4$
D: $m = 1,n = 8$

Answer 1

Hint:From the given figure it is easy to identify that this sum is related to the chapter Simultaneous Equation. In this sum, the student has to substitute the value of $x\& y$ two times in order to get $2$ equations in terms of$m\& n$. After getting the two equations the student has to solve those equations simultaneously to obtain the value of $m\& n$.

Complete step by step solution:
The first step in any simultaneous equation numerical is to bring the equation in terms of 2 unknown. In this particular problem, the student has to substitute the values of $x\& y$ and equate it to $3\& 8$to get the $2$ equations in terms of $m\& n$.
On substituting the $x = 5$& $y = 6$, we get the $1st$equation:
\[5 \times m - 6 \times n = 3...........(1)\]
On substituting the $x = 6$& $y = 5$, we get the $2nd$equation:
$6 \times m - 5 \times n = 8...........(2)$
Solving two equations simultaneously, we multiply equation $1$ by $6$& equation $2$ by $5$,
\[30 \times m - 36 \times n = 18...........(3)\]
$30 \times m - 25 \times n = 40...........(4)$
Subtracting equation $4$from equation $3$
$11 \times n = 22$
$\therefore n = 2$
Substituting $n = 2$in equation $1$, we will get the value of $m$.
\[5 \times m - 6 \times 2 = 3...........(1)\]
$\therefore 5m = 15$
$m = 3$

Answer to this question is option A: $m = 3,n = 2$

Note:
It is always advisable to solve these sums as solved in the above method. Sometimes students use the method of substitution i.e. substituting one variable in the form of another and then use that value and inputting it in the second equation to get the required value. This type of method is suitable when the constant with the variable is $1$. But if the constants are bigger, students can make mistakes while going for the substitution method. On the contrary, solving simultaneously would reduce the chances of making mistakes.