For which values of a and b does the following pair of linear equations have an infinite number of solutions?

i) For the pair of linear equations to have infinite number of solutions,a1a2=b1b2=c1c2Given equation is2x+3y=7Thusa1=2,b1=3,c1=−7We knowa2=a−b,b2=a+b,c2=−3a−b+2Therefore,2a−b=3a+b=7(3a+b−2;)⇒−6;a−2;b+4=−7a+7b⇒a−9b=−4.. (1)and−9a+3b+6=−7a−7b⇒−2;a+4b=−6;.. (2)Solving (1) and (2), we geta=5,b=1ii) For the pair of linear equations to have infinite number of solutions,a1a2=b1b2=c1c2Given equation is3x+y=1Thusa1=3,b1=1,c1=1We knowa2=2k−1;,b2=k−1;,c2=2k+1Therefore,32k−1;=1(k−1;)≠1(2k+1)⇒3k−3=2k−1;,2k+1≠k−1;⇒k=2,k≠−2;∴whenk=2then equations will have no solution