First we define the variables:
m = multiple choice questions
s = short answer questions
Next we need to satisfy 2 conditions:
1) There are a total of 40 questions. We can represent this mathematically using the variables I defined:
[tex]m+s=40[/tex]
2) The multiple-choice questions are worth 2 points and the short-answer are worth 4 points but they need to total 100 points. This can also be represented mathematically:
[tex]2m+4s=100[/tex]
By satisfying the conditions provided we were able to create the 2 equations!
[tex]m+s=40[/tex]
[tex]2m+4s=100[/tex]
An equation is formed when two equal expressions. The system of equations that can be used for the situation is x+y=40 and 2x+4y=100.
An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let the number of multiple-choice questions be represented by x, while the number of short questions is represented by y.
Given there is a total of 40 questions on a test. Therefore, the total number of questions can be written as,
Number of multiple-choice questions + Number of short questions = Total number of questions
x + y = 40
Further, given the multiple-choice questions are worth 2 points and the short answer questions are worth 4 points. There is a total of 100 points on the test. Therefore, the total points in the test can be written as,
Points of multiple-choice questions + Points of short questions = Total number of Points
2x + 4y = 100
Hence, the system of equations that can be used for the situation is x+y=40 and 2x+4y=100.
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