Cramer's Rule uses determinants to solve systems and was named after the wacky guy on Seinfeld. (OK, I made that last part up.)
Let's just do one and I'll show you how it works:
First, we'll get the determinant of the coefficient matrix -- we'll call it D:
Now, we're going to find two more determinants.
|The first one we'll call||-- here's how it goes:|
and delete the column for the x guys...
Replace that column with the " = guys " (the 7 and the -2) and you get
To get the x part of our (x, y) solution, we take