Question

Determine the number of solutions to this system of linear equations:
2x+y=6
2
𝑥
+
𝑦
=
6

4x+2y=8
4
𝑥
+
2
𝑦
=
8

Answer 1

No solutions — the system is inconsistent.

Reason: From 2x + y = 6 we get y = 6 − 2x. Substituting into 4x + 2y = 8 gives
4x + 2(6 − 2x) = 8 ⇒ 4x + 12 − 4x = 8 ⇒ 12 = 8,
a contradiction. Geometrically, the two equations are parallel lines (both have slope −2) with different intercepts, so they do not meet.