Question -
Answer -
Solution:
Given pair of linearequations is
2x + 3y = 7
2px + py = 28 – qy
or 2px + (p + q)y – 28= 0
On comparing with ax +by + c = 0,
We get,
Here, a1 =2, b1 = 3, c1 = – 7;
And a2 =2p, b2 = (p + q), c2 = – 28;
a1/a2 =2/2p
b1/b2 =3/ (p+q)
c1/c2 =¼
Since, the pair ofequations has infinitely many solutions i.e., both lines are coincident.
a1/a2 =b1/b2 = c1/c2
1/p = 3/(p+q) = ¼
Taking first and thirdparts, we get
p = 4
Again, taking last twoparts, we get
3/(p+q) = ¼
p + q = 12
Since p = 4
So, q = 8
Here, we see that thevalues of p = 4 and q = 8 satisfies all three parts.
Hence, the pair ofequations has infinitely many solutions for all values of p = 4 and q = 8.