Question

Solve the system.
2x + 3y = 5

3y = 5 – 2x
2x + 3y = 5
(0, 5/3)
∅

Answer 1

The second equation is 3y = 5 − 2x, which rearranges to 2x + 3y = 5, the same as the first. So the system reduces to one equation in two unknowns and has infinitely many solutions:

y = (5 − 2x)/3, or equivalently {(x, (5−2x)/3) | x ∈ ℝ}.

(0, 5/3) is one solution, ∅ is not.