Solve the following simultaneous linear equations:
4m + 6n = 54
3m + 2n = 28
Answers
Question :-
Solve the following simultaneous linear equations :
4m + 6n = 54
3m + 2n = 28
Answer :-
Given :-
linear equations :-
4m + 6n = 54
3m + 2n = 28
Required to find :-
- Values of m and n
Method used :-
Elimination method
Solution :-
Given linear equations :-
4m + 6n = 54
3m + 2n = 28
These are linear equations in 2 variables .
The variables are m and n .
So,
In order to solve a linear equations in 2 variables
We should use some methods in order to solve these simultaneous equations .
The method here used is called as elimination method .
So,
Consider ,
Now,
Multiply equation 1 with 3
So,
3 ( 4m + 6n ) = 3 ( 54 )
Similarly,
Multiply equation 2 with 4
So,
4 ( 3m + 2n ) = 4 ( 28 )
Now,
Subtract equation 3 and equation 4
So,
12m + 18n = 162
12m + 8n = 112
0 + 10n = 50
So,
Now substitute this value of n in equation 1
So,
4m + 6n = 54
4m + 6(5) = 54
4m + 30 = 54
4m = 54 - 30
4m = 24
Therefore,
Value of m = 6
value of n = 5
Points to remember :-
We can use different methods to solve linear equations in 2 variables .
Some of them are ;
- Eliminating method
- Substitution method
- Graphical method
- Cross multiplication method and etc.
Generally a linear equation in 2 variables should be of the form
ax + by + c = 0
Most used method to solve linear equations in 2 variables is elimination method .
Given that ,
A pair of linear equations in two variables are
4m + 6n = 54 --- (i)
3m + 2n = 28 --- (ii)
Multiply eq (i) by 3 and eq (ii) by 4 , we get
12m + 18n = 162 --- (iii)
and
12m + 8n = 112 --- (iv)
Subtract eq (iv) from (iii) , we get
➡18n - 8n = 50
➡10n = 50
➡n = 5
Put the value of n = 15 in eq (ii) , we get
➡3m + 10 = 28
➡3m = 18
➡m = 6