Math, asked by Ali012, 9 months ago

Solve the following simultaneous linear equations:

4m + 6n = 54

3m + 2n = 28​

Answers

Answered by MisterIncredible
21

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 ,

\tt{4m + 6n = 54 }{\longrightarrow{equation - 1 }}

\tt{3m + 2n = 28 }{\longrightarrow{ equation - 2 }}

Now,

Multiply equation 1 with 3

So,

3 ( 4m + 6n ) = 3 ( 54 )

\implies{\rm{ 12m + 18n = 162 }}{\longrightarrow{equation - 3 }}

Similarly,

Multiply equation 2 with 4

So,

4 ( 3m + 2n ) = 4 ( 28 )

\implies{\rm{ 12m + 8n = 112 }}{\longrightarrow{equation - 4}}

Now,

Subtract equation 3 and equation 4

So,

12m + 18n = 162

12m + 8n = 112

{(-)\;\;\;\;    (-)\;\;\;\;       (-)}

\rule{200}{2}

0 + 10n = 50

So,

\tt{ n = \dfrac{50}{10}}

\red{\underline{\tt{ n = 5 }}}

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

\tt{ m = \dfrac{24}{4}}

\red{\underline{\tt{ m = 6 }}}

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 .


CaptainBrainly: Perfect!
BrainlyConqueror0901: fantastic dude : )
Anonymous: Amazing!
Anonymous: Awesome!
MisterIncredible: Thank you all for your fabulous appreciation
Anonymous: Awesome
Answered by Anonymous
15

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

 \therefore \bold{ \sf \underline{The  \: values  \: of \:  m \:  and  \: n \:  are \:  6  \: and \:  5 \: }}


BrainlyConqueror0901: well done : )
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