You have to earn 14 more credits to graduate. You plan to take 9 more classes which are worth 1 or 2 credits. If x is the number of classes worth 1 credit, and y is the number of classes worth 2 credits, which system of equations could be used to represent this situation?

Question

A. x + y = 14
2x + y = 9

B. x + y = 14
x + 2y = 9

C. x + y = 9
x + 2y = 14

D. x + y = 9
2x + y = 14

Answer 1

To solve this, we need to create two equations based on the information given:

1. The total number of classes you plan to take is 9. This counts both 1-credit and 2-credit classes. So we have:
\( x + y = 9 \)

2. You need to earn 14 more credits to graduate. If x represents the number of classes worth 1 credit and y represents the number of classes worth 2 credits, then the total number of credits from those classes can be represented as:
\( 1x + 2y = 14 \)

Using the two equations above, we now look at the options:

A. x + y = 14 (This equation would imply we're taking 14 classes, which is incorrect)
2x + y = 9 (This doesn't match our calculations)

B. x + y = 14 (Incorrect as this implies 14 classes)
x + 2y = 9 (Doesn't match our calculations)

C. x + y = 9 (Correct number of classes)
x + 2y = 14 (Incorrect representation of the credits earned)

D. x + y = 9 (Correct number of classes)
2x + y = 14 (Correct representation of the credits earned)

The correct system of equations is represented by D:

\( x + y = 9 \)
\( 2x + y = 14 \)