How do you solve the system # -7x+y=-19# and #-2x+3y=-19#?
There's two ways in which we solve systems in general: elimination, and substitution.
We'll be using substitution to solve this system. Why? Notice that we have a single
Step 1: Solve for One Variable
Let's first write out our equations:
Now, we solve for one variable. I'm going to solve for
As you can see, that was pretty easy, and gave us a relatively nice result. This is why we chose to do substitution for this particular problem.
Step 2: Plug into Other Equation; Solve for Other Variable.
Now, let's plug in the value for
Note: Watch your signs while you do this
Combine like terms:
Step 3: Solve for First Variable
We could plug this value we found for
So, our final solutions are
You can see this graphically below. The red line is equation (1) and the blue line is equation (2):
Hope that helped :)