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

No solution

Step-by-step explanation:

Let the larger number be 'N', and smaller number be 'n'

N = 2n + 3 from the first statement

N = 2(n + 1) from the second statement

Attempt to solve them simultaneously,

2n + 3 = 2(n - 1)

2n + 3 = 2n - 2

3 = -2

A false statement, which means this situation has no solutions.

Alternate approach;

These two lines are parallel because both have a slope of 2. But their y-intercepts are different which means they are distinct and parallel, hence they will never meet. Therefore, no solutions.

Step-by-step explanation:

Let x represent the larger number.

Let y represent the smaller number.

The larger number is equal to twice a smaller number plus 3. This is expressed as

x = 2y + 3

x - 2y = 3 - - - - - - - - - - - - -1

The same number is equal to twice the sum of the smaller number and 1. This is expressed as

x = 2(y + 1)

x = 2y + 2

x - 2y = 2- - - - - - - - - - - - - - 2

Subtracting equation 2 from equation 1, it becomes

0 = 1

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