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Pair of Linear Equations in Two Variables
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27/05/2021 12:06 pm
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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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27/05/2021 12:07 pm
Given, 3y + 2x -7 =0
(a + b)y + (a-b)y – (3a + b -2) = 0
a1/a2 = 2/(a-b), b1/b2 = 3/(a+b), c1/c2 = -7/-(3a + b -2)
For infinitely many solutions,
a1/a2 = b1/b2 = c1/c2
Thus 2/(a-b) = 7/(3a+b– 2)
6a + 2b – 4 = 7a – 7b
a – 9b = -4 ……………….(i)
2/(a-b) = 3/(a+b)
2a + 2b = 3a – 3b
a – 5b = 0 ……………….….(ii)
Subtracting (i) from (ii), we get
4b = 4
b =1
Substituting this eq. in (ii), we get
a -5 x 1= 0
a = 5
Thus at a = 5 and b = 1 the given equations will have infinite solutions.