How do you solve algebraically #x+y=2# and #xy=4#?
2 Answers
If you have 2 equations you can add the left sides of the equations together and the right sides of the equations together to get a new valid equation
Substituting
For example using
we get

A very simple way to solve this is by ADDING the two equations.

The two equations are
#x+y=2# (1)
#xy=4# (2)
Adding the Left Hand Sides will give us:
Adding the Right Hand Sides will give us:
That gives us
Dividing both sides by 2, we get
Substituting
Subtracting 3 from both sides gives us
The Solution for these two equations is
 Once we arrive at a solution, it is a good idea to VERIFY our answer
Substituting
Left Hand Side:
Substituting
Left Hand Side:
We have verified our answer, and we can be sure that it's correct.