Question 1005787

x = number of 2 point questions
y = number of 3 point questions


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There are 42 questions total, so,
x+y = 42


solve for y to get
y = 42-x
y = -x+42


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There are x questions that are 2 points each. In total, we have 2x points just for these types of questions.


There are y questions that are 3 points each. In total, we have 3y points just for these types of questions.


The grand total is 2x+3y points. We're given the grand total to be 100.


So the second equation is 2x+3y = 100


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Now we will replace the y in the second equation with -x+42 then solve for x


2x+3y = 100
2x+3(-x+42) = 100
2x-3x+126 = 100
-x+126 = 100
-x+126-126 = 100-126
-x = -26
x = 26


Use this x value to find the value of y

y = -x+42
y = -26+42
y = 16


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Summary:
x = 26 and y = 16


There are 26 two point questions and 16 three point questions.