This hydraulic system should produce an output force of 50,000 newtons. How large an area should the output piston have?

Complete question is;

In a hydraulic system, a 100-newton force is applied to a small piston with an area of 0.0020 m².

This hydraulic system should produce an output force of 50,000 newtons. How large an area should the output piston have?

A2 = 1 m²

Step-by-step explanation:

Using Pascal's Law which is here applied to mechanical advantage of a hydraulic piston, we can find the area of the large piston from;

F1/A1 = F2/A2

We are given;

Force of small piston: F1 = 100 N

Area of small piston; A1 = 0.0020 m²

Force of small piston: F2 = 50000 N

Thus;

Making A2 the subject, we have;

A2 = (F2/F1)A1

A2 = (50000/100) × 0.0020

A2 = 1 m²

All you have to do is plug in the x and y values for each ordered pair into the left hand side of the equation and see if you get 15 = 15. If you do, the ordered pair is a solution; otherwise it is not a solution. For example, let's try (-2,-3); that is x = -2 and y = -3:

2x - 9y = 15
2(-2) - 9(-3) = 15
-4 - (-27) = 15
-4 + 27 = 15
23 = 15

This is obviously not true, so (-2,-3) is not a solution. Now you try it on each of the ordered pairs given in the problem statement.