Question

2x + 3y =7,(p+q) + (2p-q)y = 3(p+q+1) have infinity many solution. Find p and q

Answer 1

Infinitely many solutions

a1/a2. = b1/b2. =c1/c2

2/p+q. =3/(2p-q). = 7/21

2/p+q. = 1/3

p+q=6. ...........(1)

p=6-q

3/(2p-q) =1/3

9=2p-q. ..........(2)

9=2(6-q)-q

9=12-2q-q

9-12=-3q

q=1

substituting value in (1)

p=5

values of p and q are 5 and 1 respectively.