Question

find value of p and q which has infinite many solutions 4x+5y=2 (2p+7q)x+(p+8q)y =2q-p+1​

Answer 1

Step-by-step explanation:

Given: a1 = 4, a2 = 2p + 7q, b1 = 5, b2 = p + 8q, c1 = 2, c2 = 2q - p + 1

For Infinitely many solutions,

a1a2=b1b2=c1c2

=> 42p+7q=5p+8q=22q−p+1

Taking, 42p+7q=5p+8q

=> 4p+32q=10p+35q

=> 6p+3q=0

=> 2p+q=0 ..........(i)

Again taking, 5p+8q=22q−p+1

=> 10q−5p+5=2p+16q

=> 7p+6q=5 ............(ii)

On solving eq.(i) and (ii), we get

p=−1,q=2