System of Equations help (Urgent)

Question

I came across this question but I could not figure it out. Could you please help me and explain how to find the answer? Thanks!

Jack solved a system of equations and ended up with 3 = 5, without making any mistakes. What does this mean about the solution to the system?

Answer 1

The solution to a system of linear equations occurs at the point where the lines intersect. But two lines will never intersect if they are parallel and have different y-intercepts: For example, consider the two equations:

y = 2x + 3

y = 2x + 5

Since the two lines have the same slope (2), they are parallel. If you set them equal, you get:

2x + 3 = 2x + 5

Subtract 2x from both sides and you get:

3 = 5

which is clearly nonsense. So a nonsensical result means the two lines are parallel and never cross so there is no solution to the system of equations.

Answer 2

This means that there are no solutions to the system because this statement, 3 = 5, is not true. If the statement was true, it means that there are infinite solutions.