Question

4m+5n =7------(I)
3m+4n =5------(ii)

Answer 1

Step-by-step explanation:

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

Thus m=6 and n=5

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Answer 2

$\underline{\underline{\blue{\textbf{Step - By - Step - Explanation : -}}}}$

Equations :

⠀⠀⠀⠀⠀4m+5n =7------(I)

⠀⠀⠀⠀⠀3m+4n =5------(ii)

Multiplying equation (1) by 3 and (2) by 4

⠀⠀⠀⠀⠀[ 4m+5n = 7------(I) ]× 3

⠀⠀⠀⠀⠀[ 3m+4n = 5------(ii) ] × 4

we get,

⠀⠀⠀⠀⠀12m + 15n = 21 ......(3)

⠀⠀⠀⠀⠀12m + 16n = 20......(4)

⠀⠀⠀⠀⠀⠀--⠀⠀⠀--⠀⠀ --⠀⠀

⠀⠀⠀⠀⠀⠀⠀ ⠀⠀- n = 1

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀n = -1

Substituting value of n in equation (3)

⠀⠀⠀⠀⠀›› 12m + 15n = 21

⠀⠀⠀⠀⠀›› 12m + 15 × (-1) = 21

⠀⠀⠀⠀⠀›› 12m - 15 = 21

⠀⠀⠀⠀⠀›› 12m = 21 + 15

⠀⠀⠀⠀⠀›› 12m = 36

⠀⠀⠀⠀⠀›› m = 36/12

⠀⠀⠀⠀⠀›› m = 3

Hence

• value of n is -1
• value of m is 3

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