Question

Which of these graphs shows that the linear system y=x−2
𝑦
=
𝑥
−
2
and 3x−3y=6
3
𝑥
−
3
𝑦
=
6
has an infinite number of solutions?

Answer 1

Write the second equation as 3x−3y=6 ⇒ x−y=2 ⇒ y=x−2. The two equations are identical, so their graphs coincide. The correct graph is the one showing the single line y = x − 2 (e.g. through (0,−2) and (2,0)) — the overlapping lines indicate infinitely many solutions.