How do we use Gaussian Elimination to solve systems of equations?

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How do we use Gaussian Elimination to solve systems of equations?

In: Mathematics

I’m a math teacher! Just taught this this year.

You need to get all the leading 1s in the matrix. Then write equations and back-sub to find the values of the variables.

Guardian elimination is essentially addition and subtraction

A good way to look at it is our decimal system. You could write a 3 digit number as an equation.

So you could have

1x + 2y + 3z = 123
And
1x + 2y + 4z = 124

In these cases we can see x=100, y=10 and z= 1

So you subtract these 2 and you end up with 0x + 0y + 1z = 1.