SOLUTION: 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 depend

Algebra.Com
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(52805)   (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(13200)   (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.
RELATED QUESTIONS

Find all solutions of the given system of equations and check your answer graphically.... (answered by Alan3354,greenestamps)
Find all solutions of the given system of equations and check your answer graphically.... (answered by Boreal,Alan3354)
Find all solutions of the given system of equations and check your answer graphically.... (answered by ikleyn)
ind all solutions of the given system of equations and check your answer graphically. If... (answered by josgarithmetic)
Find all solutions of the given system of equations and check your answer graphically.... (answered by MathLover1)
I need help solving this problem: Find all solutions of the given system of equations... (answered by KMST)
Please help me with this problem: Find all solutions of the given system of equations (answered by KMST)
Solve the following system of linear equations by graphing. If there is no solution, or... (answered by HasanSahin)
solve the equations and check your solutions. if there is no solutions, say so... (answered by ewatrrr)