How solve systems of equations?

Answer 1

The answer will depend on the nature of the equations and the level of your knowledge.

Probably the simplest way to deal with a general problem is to do it graphically. As long as you can calculate the values of the equations, you can plot them and the solutions are a subset of the points of intersection.

If the equations are all linear and do have a solution then inverting the matrix of coefficients is probably simplest way. In some respects this is like

• selecting one equation,
• using it to express on variable in terms of the others,
• substituting the expression for that variable in all the other equations.

That reduces the number of equations and variables by one. Continue until you have just one variable whose value you can determine. Substitute this value in one of the last two equations and you will then have two known variables. Go back up the line until you have them all.