How to tell if a system of equations has no solution or infinitely many?

Which triangle congruence postulate or theorem justifies my claim that the steps i made using construction paper and scissors produce an isosceles triangle? was it sss, sas, asa, aas, or hl?

Solve each quadratic equation by factoring and using the zero product property. x^2 + 18x = 9x

2/3(-6y+9x) expand each expression using the distributive property