If 3 shirts and 4 caps cost $96, and 2 shirts and 5 caps cost $99, how much did each cap and each shirt cost?

Hmmm let us try again...but this time with a different strategy, by the graph method.

The system is

3x + 4y =96
2x + 5y = 99.

We find solutions of each system and then plot them on a graph.

Solutions for equation 1 = (2, 22.5) and (30, 0)
Solutions for equation 2 = (49.5 , 0) and (1, 19.4)

Now, we plot both the equations on a graph paper and note its intersecting point.

Experimentally, we find the intersecting point is (12,15)

Thus, the solution for the system is x = 12 , y = 15.

Thus, we arrive at the conclusion 1 shirt  costs 12$
1 cap costs 15$