Linear Systems: 3 Variables

Question

Three forces

F1,F2,and F3

are applied to an object. Based on Newton's laws, the following system of linear equations relates these forces, which are measured in Newtons (N). Solve the system of equations to find each force. (Note that forces may be positive or negative, depending on the direction from which they are applied to the object.)

F1 + F2 + F3 = 9

2F1 + F2 − F3 = −4

3F1 + 2F2 − F3 = −3

Answer 1

You do not indicate how you are supposed to solve these problems.

I spotted right away that you could add the first two equations and subtract the third, giving you F3 = 8

Then, substituting F3 =8, we have in the first two equations

F1+F2 = 1

2F1+F2 = 4

Subtracting the top from the bottom, we have F1 = 3; then, F2 = -2

(3, -2, 8)