Question

if the pair of linear equations 2x+3y=11 and (m+n)x+(2m-n)y=33 has infinitely many solutions then find the value of m and n

Answer 1

Answer:Step-by-step explanation

It is the case of infinitely many solutions that means the second equation is just a multiple of first equation

Therefore, ax + by = c….…(1)

Second equation is just a multiple of first equation so for that

Let Π be the multiplier

Therefore, Πax + Πby = Πc……(2)

We know that,c=11 and Πc=33

Therefore ,Π=3

a =2 and Πa = m + n

Therefore,Πa = 3*2 = 6 = m + n.....(3)

Now, b=3 and Πb = 2m - n

Therefore,Πb=3*3 = 9 =2m -n……(4)

Adding (3) and (4)

6 = m + n

9 = 2m - n

15= 3m

m = 5

Put m = 5 in (3)

6 = m + n

6= 5 + n

n= 1

Answer 2

Answer:

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Step-by-step explanation:

As we know,

infinitely many means

a1/a2=b1/b2=c1/c2

2/(m+n)=3/(2m-n)=7/21

2/(m+n)=7/21

2/(m+n)=1/3

6=m+n.............(1)

3/(2m-n)=7/21

3/(2m-n)=1/3

9=2m-n............(2)

Now on adding (1) and (2)

m+n+2m-n=6+9

3m=15

m=5

Now put m value in (1)

6=5+n

n=1