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?

Let the smaller number be x and the number be y. The first statement gives y = 2x + 3, while the second gives y = 2(x + 1) = 2x + 2. These lines have the same slope, 2, but different y-intercepts, 3 and 2, so they never intersect; therefore, no solutions are possible. The correct choice is C, “No solutions exist because the situation describes two lines that have the same slope and different y-intercepts.”

AI-written and checked against the verified answer.