Let's dive into the problem and derive the two equations that describe your winning scenario:
1. We are given that you feel confident to respond to only 12 questions. We can denote the number of questions you feel confident to answer correctly as [tex]\( x \)[/tex] and the number of questions you do not feel confident about as [tex]\( y \)[/tex].
Since you respond to a total of 12 questions, the first equation can be written as:
[tex]\[
x + y = 12
\][/tex]
2. You need 600 points to defeat Kimberly. Let's assume each correct response earns you 100 points, and each incorrect response loses you 200 points.
From this, the total points you can earn can be expressed as a function of the number of correct and incorrect responses:
[tex]\[
100x - 200y = 600
\][/tex]
These two equations represent your winning scenario:
1. [tex]\( x + y = 12 \)[/tex]
2. [tex]\( 100 x - 200 y = 600 \)[/tex]
Hence, the correct equations are:
[tex]\[
\boxed{x + y = 12}
\][/tex]
[tex]\[
\boxed{100 x - 200 y = 600}
\][/tex]
