Exploration 2.1.1.
The purpose of this problem is to formalize what you may already know (perhaps under a different name) about elementary row operations as means of solving systems of linear equations. Consider the system
We will begin by adding twice the first row to the second row, and replacing the second row with the sum.
Note that this step eliminates from the second equation. Next we divide both sides of the second equation by
We now know what is. Our next goal is to eliminate from the first equation. To this end, we subtract twice the second row from the first row and replace the first row with the difference.
Next we multiply both sides of the first equation by
Finally, we can switch the order of equations in order to display in the top row.
This solution can be written as an ordered pair