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

Explanation:

If you want to use substitution you need to convert the first equation to y=

so you can subtract x from both sides to isolate y

so now you have y=24-x

now we plug that in

to get 3x+5(24-x) =100

now we have a one variable equation

then distribute

to get 3x+120-5x=100

then combine like terms

to get 120-2x=100

then isolate the x, but we don't want to have a negative x so we add x to both sides

to get 120=100+x

then we isolate x by subtracting 100 from both sides

to get 20=x

so there are 20 3-point questions

now you can plug that in to the first equation to get y

x+y=24

(20)+y=24

subtract y from both sides to get

y=4