Question

Find the values of p and q for which the following system of linear equations has infinite number of solutions:
2x+3y=9(p+q)x-(2p-q)y=3(p+q+1)

Answer 1

Answer:

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Answer 2

p = 5/3 ; q = 1/3

Step-by-step explanation:

Given:  

2x + 3y = 9

(p+q)x +(2p-q)y = 3(p+q+1)

The system of equations has infinitely many solutions.

a1 = 2, b1 = 3, c1 = 9

a2 = p+q, b2 = +(2p-q), c2 = 3(p+q+1)

 So  a1/a2 = b1/b2 = c1/c2

 2/p+q = 3/(2p-q)

 2(2p-q) = 3(p+q)

 4p -2q = 3p + 3q

 p - 5q = 0 ---------------(1)

 Also 2/p+q = 9/3(p+q+1)

 2 (p + q+ 1) = 3 (p + q)

 2p + 2q + 2 = 3p + 3q

 p + q = 2 ------------------(2)

Subtracting (2) from (1), we get:  

     -6q = -2

Therefore q = 1/3

Substituting q in (2), we get: p + 1/3 = 2

Therefore p = 5/3