Question

Determine which system below will produce infinitely many solutions.

Answer 1

First task:
To determine this we need to make difference between system that doesn't have solution and system that has infinite number of solution. If when solving equations we get   0 = 0 that means system has infinite number of equations.
If we get 0 = some number that means that system doesn't have solution.

Multiplying first equation of second system by 2 and adding it to second equation we get 0=0 which means that this system has infinite number of solutions.

Answer is second system

Second task:
For this we need to set a system of equations and solve it. System looks like this:
x + y = 224
x*12 + y*8=2520
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x represents older than 18 and "y" 18 and younger than that.
first equation we multiply with -12 and sum it with second.
-4y = -168
y=168/4 = 42

Answer is 42.

Answer 2

-2x + 4y = 18
4x - 8y = -36

This system has infinite solutions as one equation is a factor of the other
 
for the second we can check that 
a number of visitors older than 18
b number of visitors  younger than 18

a(12) +b(8) = 2520
a + b = 224

solving the equation system we have 
that 182 visitors were 18 or younger