Question

(5) 4m + 6n=54; 3m + 2n=28​

Answer 1

Given:-

• 4m + 6n = 54;3m + 2n = 28

⠀

To find:-

• Value of m and n.

⠀

Solution:-

★ Mulitply second equation by 3 and subract first equation from it,

⠀

→ 3(3m + 2n) - (4m + 6n) = 3(28) - 54

→ 9m + 6n - 4m - 6n = 30

→ 5m = 30

→ m = 6

⠀

★ Substitute in first equation,

⠀

→ 4(6) + 6n = 54

→ 6n = 54 - 24

→ 6n = 30

→ n = 5

⠀

Hence,

• m = 6
• n = 5

Answer 2

$\huge\bold{Question :- }$

Solve the following simultaneous linear equations :

4m + 6n = 54

3m + 2n = 28

$\huge\bold{Answer :- }$

$\sf\underline\red{Given:}$

linear equations :-

4m + 6n = 54

3m + 2n = 28

$\sf\underline\green{Required~ to~ find :-}$

• Values of m and n

$\sf\underline\orange{Method~use :-}$

• 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 .

$\sf\underline\pink{so,}$

• 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 $\sf\underline\blue{elimination~method }$

$\sf\underline\pink{so,}$

Consider,

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

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

$\bf\underline{Now,}$

• Multiply equation 1 with 3

$\sf\underline\pink{so,}$

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

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

Similarly

• Multiply equation 2 with 4

$\sf\underline\pink{so,}$

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

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

$\bf\underline{Now,}$

• Subtract equation 3 and equation 4

$\sf\underline\pink{so,}$

12m + 18n = 162

12m + 8n = 112

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

$\rule{200}{2}$

0 + 10n = 50

$\sf\underline\pink{so,}$

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

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

Now substitute this value of n in equation 1

$\sf\underline\pink{so,}$

4m + 6n = 54

4m + 6(5) = 54

4m + 30 = 54

4m = 54 - 30

4m = 24

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

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

$\huge\bold{Therefore :- }$

• Value of m = $\sf\underline\pink{6}$

• value of n = $\sf\underline\pink{5}$