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Question

Question 2 (i)
For which values of ‘a’ and ‘b’ does the following pair of linear equations have an infinite number of solutions?
2x + 3y =7
(a - b)x + (a + b)y = 3a +b - 2


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Solution

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

Compare the given equations with

a1x+b1y+c1=0 and a2x+b2y+c2=0.

a1a2=2ab
b1b2=3a+b
c1c2=7(3a+b2)=7(3a+b2)
For infinitely many solutions, a1a2=b1b2=c1c2
2ab=73a+b2
2(3a + b - 2) = 7 (a-b)
6a + 2b - 4 = 7a - 7b
a - 9b = -4 ... (i)
2ab=3a+b
2a + 2b = 3a - 3b
a - 5b = 0 ... (ii)
Subtracting equation (i) from (ii), we get
4b = 4
b = 1
Putting this value in equation (ii), we get
a - 5 × 1 = 0
a = 5
Hence, a = 5 and b = 1 are the values for which the given equations give infinitely many solutions.


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