Question:
Find the value of a and b for which the following system of equations has infinitely many solutions: 2x 3y=7 (a-1)x (a 1)y=3a-1
Answer:
Given, equations are:
2x + 3y = 7
(a - 1)x + (a + 1)y = 3a - 1
Given, system of equations has infinitely many solution.
So, 2/(a - 1) = 3/(a + 1) = 7/(3a - 1)
=> 2/(a - 1) = 3/(a + 1)
=> 2(a + 1) = 3(a - 1)
=> 2a + 2 = 3a - 3
=> 3a - 2a = 2 + 3
=> a = 5
So, the value of a is 5
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