To determine the system of equations for the given situation, let's break down the problem step-by-step.
1. Define the variables:
- Let [tex]\( m \)[/tex] be the number of multiple-choice questions.
- Let [tex]\( s \)[/tex] be the number of short answer questions.
2. Translate the word problem into mathematical equations.
First, we know the total number of questions on the test:
[tex]\[ m + s = 30 \][/tex]
Second, we know the total number of points on the test. Multiple-choice questions are worth 2 points each, and short answer questions are worth 6 points each. The total points accumulated from both types of questions must sum up to 100:
[tex]\[ 2m + 6s = 100 \][/tex]
Hence, the correct system of equations to represent the situation is:
[tex]\[
\begin{cases}
m + s = 30 \\
2m + 6s = 100
\end{cases}
\][/tex]
This system accurately models the given scenario. It tells us that the sum of multiple-choice and short answer questions is 30, and the total points from these questions sum to 100.
