, 0 For which values of a and b does the lollowinfinite number of solu

1.	, 0 For which values of a and b does the lollowinfinite number of solutions?2x + 3y=7
Answer» The pair of linear equations represented by these lines a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 For infinite many solutionsa1/a2 = b1/b2 = c1/c2 Given equations2x + 3y - 7 = 0(a-b)x + (a+b)y - (3a + b - 2) = 0 Then, 2/(a-b) = 3/(a + b) = 7/(3a + b-2) 2(a + b) = 3(a - b).......(1)3/(a+b) = 7/(3a + b - 2).......(2)2a + 2b = 3a - 3ba = 5b Put value of a = 5b in eq(2),We get3(3a + b - 2) = 7(a + b) 95b + 3b - 6 = 75b + 7b48b - 6 = 42b48b - 42b = 66b = 6b = 6/6 = 1 a = 5b = 5*1 = 5

, 0 For which values of a and b does the lollowinfinite number of solutions?2x + 3y=7

Answer»

The pair of linear equations represented by these lines a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0

For infinite many solutionsa1/a2 = b1/b2 = c1/c2

Given equations2x + 3y - 7 = 0(a-b)x + (a+b)y - (3a + b - 2) = 0

Then, 2/(a-b) = 3/(a + b) = 7/(3a + b-2)

2(a + b) = 3(a - b).......(1)3/(a+b) = 7/(3a + b - 2).......(2)2a + 2b = 3a - 3ba = 5b

Put value of a = 5b in eq(2),We get3(3a + b - 2) = 7(a + b) 9*5b + 3b - 6 = 7*5b + 7b48b - 6 = 42b48b - 42b = 66b = 6b = 6/6 = 1

a = 5b = 5*1 = 5