How do you solve the system of equations when you have 4 equations with 4 unknowns?

Answer 1

There are several ways to do it - depending, in part, on the kind of equations. Sophisticated methods exist specifically for linear equations, among others.

However, for a start, you can combine equations (1) and (2), eliminating one variable; the same for equations (2) and (3), and for equations (3) and (4) (eliminating the same variable in every case). That leaves you with 3 equations with 3 variables.

Similarly, reduce the 3 equations in 3 variables, to 2 equations in 2 variables (eliminating the same variable in every case). Combine those into a single equation with 1 variable.

Example for eliminating a variable:

(Eq. 1) 5a + 3b - 3c + 8d = 28

(Eq. 2) 8a - 3b + 8c - 6d = 8

If you just add up the equations, you eliminate variable b. If you want to eliminate variable a, multiply the first equation by 8, and the second by (-5), then add the resulting equations.