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 solutions exist because the situation describes two lines that have the same slope and different y-intercepts.

Step-by-step explanation:

Let n equal the number, and let x equal the smaller number. Let's put this into equation form to make everything easier to understand.

x < n

n = 2x + 3

n = 2x + 1

Note how n equals two different things. In other words, how can n equal 2x + 3, but also equal 2x + 1? The equations have different y-intercepts but the same slope, meaning there are no solutions, or points where the lines would intercept. The only answer that highlights this is the third option.

To further clear things up, let's go through the other answers to make sure we're correct.

Answer 1: Two situations do not describe the exact same line; all parts of the question are unique.

Answer 2: The equations do not have different slopes, so this reasoning is invalid.

Answer 4: The situations describe two equations with the same slope but different y-intercept, not the other way around. In equation form, 2 = 2, but 3 ≠ 1.

Therefore, the only correct answer is option 3.

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step-by-step explanation:

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multiply then divide

step-by-step explanation: