What is the difference between an equation with no solution and an equation with a infinitely many solutions? Please give an example in your response.
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No solution would mean that there isn't an answer to the equation. it would be impossible for the equation to be true. Infinite/many solutions means that any value for the variable would make the equation true.

Example:

No solution:

0 = 0, x = x

2x + 4y= 8

x + 2y = 4

Many solutions:

2 = 5

3x + 2y = 5

6x + 4y = 8

4 and 5)16.97 or 12√2

6)15.59 or 9√3

7)y = 15.59 or 9√3     x =27

8)17.80