Question

The graph of a system of equations with the same slope will have no solutions.

Always

Sometimes

Never

Answer 1

How many solutions does the following system have:

y = 5x + 2
y = 5x + 6

Answer 2

always

Answer 3

@Directrix

Answer 4

I do not agree with Always as the answer.

Consider this system:

x + y = 2
3x + 3y = 6
-----------

How many solutions does it have?

Answer 5

never

Answer 6

In this case,
y = 5x + 2
y = 5x + 6

there were no solutions because the lines are parallel.

Answer 7

In this case,
x + y = 2
3x + 3y = 6
-----------

there were infinitely many solutions because the two equations are equations of the same line. So, they intersect at every point. And, a line has infinitely points.

So, what is left for the correct answer.