Question

the lines $2x - y = 8$ and $4x - 2y = 16$ intersect at _______.

a. 2 points

b. 1 point

c. an infinite number of points

d. there are no intersection points.

Explanation:

Step1: Simplify the second equation

We have the second equation \(4x - 2y = 16\). If we divide the entire equation by 2, we get \(2x - y = 8\), which is the same as the first equation \(2x - y = 8\).

Step2: Analyze the relationship between the two lines

Since both equations represent the same line (they are equivalent), every point on the first line is also on the second line. So, the two lines coincide, meaning they intersect at an infinite number of points.

Answer:

C. an infinite number of points