Question 1110996: Find all solutions of the given system of equations and check your answer graphically. HINT [See Examples 2–5.] (If there is no solution, enter NO SOLUTION. If the system is dependent, express your answer in terms of x, where y = y(x).)
x + y = 16
x − y = 26
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52903)   (Show Source):
You can put this solution on YOUR website! .
This system of equations is the simplest example of the system of 2 equations in two unknowns.
In addition, it is the MOST POPULAR example.
When you see such a system, add the two equations MOMENTARILY / immediately / INSTANTLY.
You will get
2x = 16 + 26 = 42 ====> x =  = 21.
Half of the solution is just DONE.
Now from either of the two original equations find y.
For example, from the first equation y = 16 - 21 = -5.
Answer. x= 21, y = -5.
The solution is completed.
Answer by greenestamps(13215)  (Show Source):
You can put this solution on YOUR website!
Here is a way to solve this kind of problem quickly with some mental arithmetic and a bit of logical reasoning.
Think of the problem this way: You are starting at some number x. If you go distance y in one direction you get to 16; if you go the same distance the other direction, you get to 26.
Logical reasoning tells you the place you started, x, has to be halfway between 16 and 26.
So x is 21.
Then the distance from 21 to either 16 or 26 is 5; since you added the second number to get from 21 to 16 and subtracted the second number to get from 21 to 26, the second number is negative. So y = -5.
The two numbers are 21 and -5.
This solution is virtually identical to the solution provided by the other tutor, without the formal algebra.
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