How Do I Solve Linear Equations with Variables and Coefficients?

[Ray Vickson]

That is definitely going to take some getting used to. My book is called Basic Mathematics by Lang and he teaches the shorter way. I'm on to solving linear equations using 3 variables and instead of having 2 equations, we now have 3. I can solve them using my method but how does the Gaussian method handle 3 equations? While it may be simpler I find it faster to use my method and I can easily deal with 3 equations without much work at all.

The Gaussian method handles 1000 equations in 1000 variables in just the same way as 2 equations in 2 variables. You just use the equations to eliminate variables one-by-one.

I have already pointed out to you that the Gaussian elimination method is equivalent to yours. It just arranges things in a slightly different way.

 

[vanceEE]

That is definitely going to take some getting used to. My book is called Basic Mathematics by Lang and he teaches the shorter way. I'm on to solving linear equations using 3 variables and instead of having 2 equations, we now have 3. I can solve them using my method but how does the Gaussian method handle 3 equations? While it may be simpler I find it faster to use my method and I can easily deal with 3 equations without much work at all.

You would handle them the same way; by eliminating variables by substitution. I suggest that you take the time to practice a few problems using this method. Being familiar with using direct substitution is essential for dealing with linear equations and any other higher maths you may encounter in the future.