SOLUTION: the sum of two numbers is 255. when the smaller number is subtracted from the larger, the result is -39.find the numbers

Question 99863: the sum of two numbers is 255. when the smaller number is subtracted from the larger, the result is -39.find the numbers
Found 4 solutions by stanbon, jim_thompson5910, checkley71, doukungfoo:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
the sum of two numbers is 255. when the smaller number is subtracted from the larger, the result is -39.find the numbers
---------------
x+y=255
x-y=-39
------------
Add the two equations to get:
2x = 216
x = 108
y = 147
================
Cheers,
Stan H.
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

Solved by pluggable solver: Solving a linear system of equations by subsitution

Lets start with the given system of linear equations

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

Solve for y for the first equation

Subtract from both sides

Divide both sides by 1.

Which breaks down and reduces to

Now we've fully isolated y

Since y equals we can substitute the expression into y of the 2nd equation. This will eliminate y so we can solve for x.

Replace y with . Since this eliminates y, we can now solve for x.

Distribute -1 to

Multiply

Reduce any fractions

Add to both sides

Combine the terms on the right side

Now combine the terms on the left side.

Multiply both sides by . This will cancel out and isolate x

So when we multiply and (and simplify) we get

<---------------------------------One answer

Now that we know that , lets substitute that in for x to solve for y

Plug in into the 2nd equation

Multiply

Subtract from both sides

Combine the terms on the right side

Multiply both sides by . This will cancel out -1 on the left side.

Multiply the terms on the right side

Reduce

So this is the other answer

<---------------------------------Other answer

So our solution is

and

which can also look like

(,)

Notice if we graph the equations (if you need help with graphing, check out this solver)

we get

graph of (red) and (green) (hint: you may have to solve for y to graph these) intersecting at the blue circle.

and we can see that the two equations intersect at (,). This verifies our answer.

-----------------------------------------------------------------------------------------------
Check:

Plug in (,) into the system of equations

Let and . Now plug those values into the equation

Plug in and

Multiply

Add

Reduce. Since this equation is true the solution works.

So the solution (,) satisfies

Let and . Now plug those values into the equation

Plug in and

Multiply

Add

Reduce. Since this equation is true the solution works.

So the solution (,) satisfies

Since the solution (,) satisfies the system of equations

this verifies our answer.

So the two numbers are 108 and 147
Answer by checkley71(8403)   (Show Source): You can put this solution on YOUR website!
X+Y=255 OR X=255-Y
Y-X=-39 NOW REPLACE X WITH (255-Y) & SOLVE FOR FOR Y
Y-(255-Y)=-39
Y-255+Y=-39
2Y=-39+255
2Y=216
Y=216/2
Y=108 ANSWER FOR THE LARGER NUMBER.
Y-108=255
X=255-108
X=147 FOR THE SMALLER NUMBER.
--------------------------------------------------------------------
THIS WORKS OUT MATHEMATICALLY BUT NOT LOGICALLY.
108 IS NOT A LARGER NUMBER THAN 147!!!!!!!!

Answer by doukungfoo(195)   (Show Source): You can put this solution on YOUR website!
First set some variables
Let the first number = x
Let the second number = y
Given: sum of two numbers is 255
so
x + y = 255
Given: the differenc of two numbers is -39
so
x - y = -39
Now set the fist equation equal to x
so
x + y = 255
x = 255 - y
Now replace the x in x - y = -39 with 255 - y
so
x - y = -39
255 - y - y = -39
255 - 2y = -39
-2y = -39 - 255
-2y = -294

y = 147
Now we have found one of the numbers to be 147
Next we can use that to find the other number
so we know from the given that x + y = 255
replace y with 147 and solve for x
x + y = 255
x + 147 = 255
x = 108
Now we found the other number to be 108
So we x = 108 and y = 147
To check our results just plug the values for x and y into
x + y = 255
and
x - y = -39
so here we go
x + y =255
108 + 147 = 255
255 = 255
It works so lets try the other one
x - y = -39
108 - 147 = -39
-39 = -39
This works too. So we know that we have successfully solve the problem.

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