Question

x-2y=6 and 3x-6y=18

has how many solutions?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine how many solutions this system of equations has, we can begin by observing the two equations:

1) x - 2y = 6
2) 3x - 6y = 18

We can simplify equation 2) by dividing each term by 3:

2) (3/3)x - (6/3)y = 18/3
x - 2y = 6

We see that equation 2) is equivalent to equation 1). Therefore, these two equations represent the same line.

Since the equations represent the same line, they intersect at every point on the line. Therefore, there are infinite solutions to this system of equations.