Question

The best answer gets 100 points. A number is equal to twice a smaller number plus 3. The same number is equal to twice the sum of the smaller number and 1. How many solutions are possible for this situation?

Infinitely many solutions exist because the two situations describe the same line.
Exactly one solution exists because the situation describes two lines that have different slopes and different y-intercepts.
No solutions exist because the situation describes two lines that have the same slope and different y-intercepts.
Exactly one solution exists because the situation describes two lines with different slopes and the same y-intercept.

Answer 1

No solutions exist because the situation describes two lines that have the same slope and different y-intercepts.

Explanation:

Let larger number be X and smaller one be Y.

The two equations are :-

X = 2Y + 3

X = 2Y + 1

As you can tell, the slopes are the same and the y-intercepts are different. So, they will not intersect. Therefore, no solutions exist for this situation.