How to prove an equation has infinitely many solutions?

Answer 1

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.