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How to prove an equation has infinitely many solutions?

In: Math and Arithmetic, Algebra, Calculus [Edit categories]

Answer:

let a1 and a2 be x-co efficient of first and second equations receptively.
let b1 and b2 be y-coefficients of first and second equations repectively.
let c1 and c2 be the constants of first and second equations repectively.

so to prove that a eq. has infinite solutions the foll. must be true:
a1/a2 = b1/b2 = c1/c2

eg: 10x + 6y = 14 - 1st eq.
5x + 3y = 7 - 2nd eq.

a1/a2=b1/b2=c1/c2 - 10/5=6/3=14/7= 2

So the above example has infinitely many sols.

First answer by ID1975608059. Last edit by ID1975608059. Question popularity: 1 [recommend question].

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