x-y=3 2x=2y+6 The system of equations above has how many solutions? (A) None (B) Exactly one (C) Exactly two (D) Exactly three (E) Infinitely many The answer should be A, but the original answer says "E". Can anyone explain?

When 2 lines have the same equation, they have infinite solutions. When 2 lines are parallel, they have no solution. (for lines to be parallel, the constant term should be different) In the given question, the lines are coincident. Hence infinite solutions

Hi, The conditions are basically as below: The pair of linear equations represented by these lines a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 (a) If , a1/a2 = b1/b2 = c1/c2 then the pair of linear equations has infinitely many solutions. (b) If , a1/a2 = b1/b2 (not equal to) c1/c2 then the pair of linear equations has no solution. AS condition a is satisfied it has infinitely many solutions. look at it as this way, you have two equations which basically are one and the same(divide second equation by 2). thus we have, x - y = 2. This equation has infinite solutions as you may agree. Hope this helps.

Thank you very much.....Its much clear now.... I was wandering with "None" & "Infinitely many".....Now ok shankar.ashwin wrote:When 2 lines have the same equation, they have infinite solutions. When 2 lines are parallel, they have no solution. (for lines to be parallel, the constant term should be different) In the given question, the lines are coincident. Hence infinite solutions