a. Visually what does it mean for a pair of linear equations to have an infinite amount of solutions?

Question

b. Visually what does it mean for a pair of linear equations to have zero solutions?

Please help! Much needed help and explanation would be appreciated :)

Answer 1

a.

When a lines overlap completely.

For example:

27 x + 18 y = 24

9 x + 6 y = 8
_____________

When you divide the first equation by 3 it will be:

9 x + 6 y = 8

In other words if both equations are same equation a pair of linear equations to have an infinite amount of solutions.

b.

This is the case where the lines are parallel and do not have a single point where they touch each other.

When there is no solution a parallel line has an identical slope.

y = m x + c1

and

y = m x + c2

for example:

y = 2 x + 1

and

y = 2 x - 7