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