Question

Determine the number of solutions to this system of linear equations (0, 1, ∞)
(
0
,

1
,

∞
)
:

y=7x+8
𝑦
=
7
𝑥
+
8


−7x+y=−8

Answer 1

0 (no solutions).

Reason: y = 7x + 8 and −7x + y = −8 ⇒ y = 7x − 8. These are two parallel lines with the same slope 7 but different y‑intercepts, so they never meet. Substitution gives 8 = −8, a contradiction.