Question

If a system of linear equations has no solution what does that tell you about the slopes and y - intercepts of the graphs equations?

Answer 1

Let's write a system of generic linear equations:
ax + by = c
dx + ey = f
A system without solution:
It occurs when the system of equations has the coefficients of x and y proportional to each other, but not proportional to the free terms. That is to say:
(a) / (d) = (b) / (e) ≠ (c) / (f)
That is, the slopes are the same.
The cut point with y is different.
Answer:
The slopes are the same.
The cut point with y is different.