If two distinct lines intersect, which is NOT necessarily true?

Which values for a and b will create infinitely many solutions for this system of equations? ax-y=8 2x+y=b

Ernest is purchasing a $175,000 home with a 30-year mortgage. he will make a $15,000 down payment. use the table below to find his monthly pmi payment.

In the figure below, ∠dec ≅ ∠dce, ∠b ≅ ∠f, and segment df is congruent to segment bd. point c is the point of intersection between segment ag and segment bd, while point e is the point of intersection between segment ag and segment df. the figure shows a polygon comprised of three triangles, abc, dec, and gfe. prove δabc ≅ δgfe.