Question

How many intersections are there of the graphs of the equations below? One-halfx + 5y = 6 3x + 30y = 36 none one two infinitely many

Answer 1

infinitely many

Explanation:

You have the system

(1/2)x + 5y = 6

3x + 30y = 36

Multiplying the first equation by 6 results in 3x + 30y = 36, which is exactly the same as the second equation. The two graphs coincide, and so there are infinitely many solutions to this system

Answer 2

infinitely many

Explanation:

• 1/2x + 5y = 6 ⇒ x+10y=12
• 3x + 30y = 36 ⇒ x+10y=12

As we see, these are equal lines, they overlap, so there are infinitely many intersections