Question

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

So the equations are

• a=2b+3
• a=2(b+1)=2b+2

Equate and solve

• 2b+3=2b+2
• 3=2

No solutions

C

Answer 2

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

Explanation:

Let the numbers are x and y.

Translate below wording into equations

A number is equal to twice a smaller number plus 3:

• x = 2y + 3

The same number is equal to twice the sum of the smaller number and 1:

• x = 2(y + 1)

Solve the system by substitution:

• 2y + 3 = 2(y + 1)
• 2y + 3 = 2y + 2
• 3 = 2

False equation, so no solution.

Correct choice is C.