Question

Find the value of m and n 3x+4y=12(m+n)x+2(m-n)Y=5m-1

Answer 1

Answer:

m = 5 & n = 1

Step-by-step explanation:

Find the value of m and n 3x+4y=12(m+n)x+2(m-n)Y=5m-1

complete question is find values of m&n for infinite solution

to have infinite solutions

both equation should be same

(m+n)x + 2(m-n)y = 5m-1

should be equivalent to 3x + 4y = 12

=> k*3x + k*4y = k*12 where k is any variable

=> (m+n)/3 = 2(m-n)/4 = (5m-1)/12 = k

Multiplying each with 12

=> 4m + 4n = 6m - 6n = 5m -1 = 12k

taking 1st 2 equations

4m + 4n = 6m - 6n

=> 10n = 2m

=> m = 5n   - eq A

taking 1st & 3rd

4m + 4n = 5m-1

=> m = 4n + 1  - eq B

equating value of m  from eq A & eq B

5n = 4n + 1

=> n = 1

putting value of n in eq A

m = 5*1 = 5

Hence value of m = 5 & n = 1