Question

For what values of a and b does the following pair of linear equations has a infinite number of solutions: 2x+3y=7; a(x+y)-b(x-y)=3a+b-2.

Answer 1

 eq 1: 2x + 3y = 7

eq 2 : a(x + y) - b(x - y) = 3a + b - 2 ⇒  x(a - b) + y(a + b) = 3a + b - 2

for two lines to have infinite solutions 2 lines must b coincident

⇒ coeff of x in (1) / coeff of x in (2) =  coeff of y in (1) / coeff of y in (2) = constant in (1) / constant in (2)

⇒ 2/a - b = 3/a+b = 7/3a+b-2

solving above will fetch u two equations
9b - a = 4 ..........(3)      and      a - 2b = 3  ...........(4)

substituting a = 3+ 2b in (3) and solving

gives a = 5 and b = 1

hope u'll get it  ........

any queries please ask .........

Answer 2

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$<marquee direction="left">$Hope it helps^_^