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

To solve this, we have to subtract these two equation to make Xs or Ys of two equations same. So if we multiply the first equation and 3 to make the same with other equation,

3x+3y=72

3x+5y=100

If we subtract two equations,

3x+3y=72

- 3x+5y=100

-2y=-28

y=14

So if we put this on the fir equation,

x+14=24

x=10

So the answer is the second one