SOLUTION: The sum of two numbers is 1. Their difference is 3. What is the smaller of the two numbers?

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Question 145788: The sum of two numbers is 1. Their difference is 3. What is the smaller of the two numbers?
Found 2 solutions by jim_thompson5910, jojo14344:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"The sum of two numbers is 1." translates to x%2By=1


"Their difference is 3." translates to x-y=3



Start we have the system of equations:

system%28x%2By=1%2Cx-y=3%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=1 Start with the first equation


y=1-x Subtract x from both sides


y=-x%2B1 Rearrange the equation



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

Since y=-x%2B1, we can now replace each y in the second equation with -x%2B1 to solve for x



x-highlight%28%28-x%2B1%29%29=3 Plug in y=-x%2B1 into the first equation. In other words, replace each y with -x%2B1. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



x%2Bx-1=3 Distribute the negative


2x-1=3 Combine like terms on the left side


2x=3%2B1Add 1 to both sides


2x=4 Combine like terms on the right side


x=%284%29%2F%282%29 Divide both sides by 2 to isolate x



x=2 Divide





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


So the first part of our answer is: x=2









Since we know that x=2 we can plug it into the equation y=-x%2B1 (remember we previously solved for y in the first equation).



y=-x%2B1 Start with the equation where y was previously isolated.


y=-%282%29%2B1 Plug in x=2


y=-2%2B1 Multiply


y=-1 Combine like terms



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


So the second part of our answer is: y=-1









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

So our answers are:

x=2 and y=-1



So the smaller of the two numbers is -1

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!
Well, Let "x" be the 1st #
"y" be the 2nd number
In 1st condition, %22x%2By=1%22 -------------eqn 1
In 2nd condition, %22x-y=3%22 -------------eqn 2
In eqn 1 we get %22x=+1-y%22 right? substitute this to eqn 2,
1-y-y=3
2y=-2
y=+-1
And the other # as per eqn 1, x%2B%28-1%29=1
x=1%2B1+=+2
So, the smaller # is y=+-1
In doubt? Go either eqn, okay we use eqn 2,
x-y=3
2-%28-1%29=3
2%2B1=3
3=3
Thank you,
Jojo