Question

Find the values of m and n for wch the following system of linear equations has infinitely many solutions 3x+4y=12 (m+n)x + 2(m-n)y = (5m-1)

Answer 1

Answer:

Step-by-step explanation:

Hope this will u

Answer 2

Answer:

m = 5 & n = 1

Step-by-step explanation:

Find the values of m and n for wch the following system of linear equations has infinitely many solutions 3x+4y=12 (m+n)x + 2(m-n)y = (5m-1)

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

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

Multiplying each with 12

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

taking 1st 2

4m + 4n = 6m - 6n

=> 10n = 2m

=> m = 5n

taking 1st & 3rd

4m + 4n = 5m-1

=> m = 4n + 1

equating value of m

5n = 4n + 1

=> n = 1

m = 5n = 5 * 1 = 5

Hence m = 5 & n = 1

Verification of answer:

putting these value we get

6x + 8y = 24

dividing by 2

3x + 4y = 12

Hence verified