Question

A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation. x + y = 24 3x + 5y = 100 What does the solution of this system indicate about the questions on the test? The test contains 4 three-point questions and 20 five-point questions. The test contains 10 three-point questions and 14 five-point questions. The test contains 14 three-point questions and 10 five-point questions. The test contains 20 three-point questions and 8 five-point questions.

Answer 1

X + y = 24....multiply by -3
3x + 5y = 100
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-3x - 3y = - 72 (result of multiplying by -3)
3x + 5y = 100
----------------add
2y = 28
y = 28/2
y = 14 <== 5 pointers

x + y = 24
x + 14 = 24
x = 24 - 14
x = 10 <== 3 pointers

Answer 2

X + y = 24
3x + 5y = 100
x=24-y
3*(24-y)+5y=100
x=10
y=14