Question

Determine the number of solutions to this system of linear equations:
y=x+5
𝑦
=
𝑥
+
5

y=−x+5
𝑦
=
−
𝑥
+
5

Answer 1

One. Solve by setting the right-hand sides equal:
x + 5 = −x + 5 ⇒ 2x = 0 ⇒ x = 0.
Then y = x + 5 = 5. The lines intersect at the single point (0, 5).