Question

5. Priya buys 2.4 lb of bananas and 3.6 lb of grapes for $9.38 at a grocery

store. At the same grocery store, Andre buys 1.2 lb of bananas and 1.8 lb
of grapes for $4.69.

This information can be represented by the following
system of equations:
[2.4b +3.6g = 9.38
(1.26 +1.8g = 4.69

What happens when you try to solve the system of equations using
elimination? Explain or show your thinking.

Answer 1

It appears there is a minor issue with the equations you've provided. I believe there might be a typo in the second equation. The corrected system of equations should be:

1. 2.4b + 3.6g = 9.38

2. 1.2b + 1.8g = 4.69

Now, let's attempt to solve this system of equations using the elimination method. The elimination method involves adding or subtracting the equations to eliminate one of the variables and then solving for the remaining variable.

In this case, we'll first multiply the second equation by 2 to make it easier to eliminate one of the variables:

1. 2.4b + 3.6g = 9.38

2. 2.4b + 3.6g = 9.38

Now, when we subtract the second equation from the first equation, the variable 'b' will be eliminated:

(2.4b + 3.6g) - (2.4b + 3.6g) = 9.38 - 9.38

0 = 0

This result means that both equations represent the same line or are linearly dependent. In other words, the two equations represent the same relationship between 'b' and 'g. There is no unique solution to this system, and it implies that the information provided might not be entirely accurate or consistent.

In practical terms, it suggests that either there is an issue with the data, or the numbers provided are rounded or approximated, making it challenging to find a precise solution. The problem could be due to measurement errors or other inaccuracies in the data.

Explanation: