Question

Values of a and b for which the following pair of linear equations have an infinite number of solutions are
2x + 3y = 7
(a-b)x + (a+b)y = 3a + b -2.
a. a = -5, b = 1.
b. a = 5, b = -1.
c. a = 5, b = 1.
d. a = -5, b = -1.

{ALIGARH MUSLIM UNIVERSITY ENTRANCE TEST, CLASS XI}

Answer 1

i think there is something wrong but i am dam sure that the process is totally right

Answer 2

Hey Rehan and Others......

Two equations are ...
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2x + 3y = 7
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(a- b )x + (a + b ) y = 3a + b - 2

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If a pair of linear equations have infinite solutions .... then...

$\frac{ a_{1} }{ a_{2}} = \frac{ b_{1} }{ b_{2} } = \frac{ c_{1}}{ c_{2} } \: \\ \\ \frac{2}{(a - b)} = \frac{3}{(a + b)} = \frac{7}{3a + b - 2} \\ \\ take \: first \: two..... \\ 2a + 2b = 3a - 3b \\ \\ 5b = a \\ \\ \frac{a}{b} = \frac{5}{1}$


Therefore ,

a = 5

b = 1

Your answer is option (c )

hope it helps