SOLUTION: I want to solve the problem: The sum of the real numbers {x} and {y} is {11}. Their difference is {5}. What is the value of {xy}?: The sum of the real numbers {x} and {y} is {11

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: I want to solve the problem: The sum of the real numbers {x} and {y} is {11}. Their difference is {5}. What is the value of {xy}?: The sum of the real numbers {x} and {y} is {11      Log On


   

Question 164346: I want to solve the problem:
The sum of the real numbers {x} and {y} is {11}. Their difference is {5}. What is the value of {xy}?: The sum of the real numbers {x} and {y} is {11}. Their difference is {5}. What is the value of {xy}?
I found the answer:
8+3=11
8-3=5
x=8
y=3
xy=24
But, I would like to know how the #'s of 8 and 3 were determined.
Also, I am an older student about to enter college. I need to know the best instructional method for beginning to intermediate algebra. I did not do well with it in high school which was a long time ago.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let "x" and "y" be the two numbers.


So the "sum of the real numbers {x} and {y} is {11}" translates to the equation x%2By=11 and "Their difference is {5}" translates to x-y=5


So we have the system of equations:

system%28x%2By=11%2Cx-y=5%29


Let's solve the system by use of substitution.


Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.




So let's isolate y in the first equation

x%2By=11 Start with the first equation


y=11-x Subtract x from both sides


y=-x%2B11 Rearrange the equation


---------------------

Since y=-x%2B11, we can now replace each y in the second equation with -x%2B11 to solve for x



x-highlight%28%28-x%2B11%29%29=5 Plug in y=-x%2B11 into the second equation. In other words, replace each y with -x%2B11. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



x%2Bx-11=5 Distribute the negative


2x-11=5 Combine like terms on the left side


2x=5%2B11Add 11 to both sides


2x=16 Combine like terms on the right side


x=%2816%29%2F%282%29 Divide both sides by 2 to isolate x



x=8 Divide





-----------------First Answer------------------------------


So the first part of our answer is: x=8









Since we know that x=8 we can plug it into the equation y=-x%2B11 (remember we previously solved for y in the first equation).



y=-x%2B11 Start with the equation where y was previously isolated.


y=-%288%29%2B11 Plug in x=8


y=-8%2B11 Multiply


y=3 Combine like terms



-----------------Second Answer------------------------------


So the second part of our answer is: y=3









-----------------Summary------------------------------

So our answers are:

x=8 and y=3


So the two numbers are 8 and 3