SOLUTION: I don't understand this method of solving? could you show me both parts of this problem in the long form for my reference. Solving: 4x+9y = 395 1x+y = 80 Us

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: I don't understand this method of solving? could you show me both parts of this problem in the long form for my reference. Solving: 4x+9y = 395 1x+y = 80 Us      Log On


   

Question 166627: I don't understand this method of solving? could you show me both parts of this problem in the long form for my reference.
Solving:
4x+9y = 395
1x+y = 80

Using Substitution Method.
Expressing x as a function of y (from the first equation) x = (395 -9y)/4
Substituting this expression into the second equation:
1(395+9y)/4+y = 80
Simplifying this expression:
(-5)y = -75

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: I'm going to make the first equation x%2By+=+80 and the second equation 4x%2B9y=395 (it is valid to relabel the equations)




Start with the given system of equations:

system%28x%2By=80%2C4x%2B9y=395%29



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=80 Start with the first equation


y=80-x Subtract x from both sides


y=-x%2B80 Rearrange the equation


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

Since y=-x%2B80, we can now replace each y in the second equation with -x%2B80 to solve for x



4x%2B9highlight%28%28-x%2B80%29%29=395 Plug in y=-x%2B80 into the second equation. In other words, replace each y with -x%2B80. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



4x%2B%289%29%28-1%29x%2B%289%29%2880%29=395 Distribute 9 to -x%2B80


4x-9x%2B720=395 Multiply


-5x%2B720=395 Combine like terms on the left side


-5x=395-720Subtract 720 from both sides


-5x=-325 Combine like terms on the right side


x=%28-325%29%2F%28-5%29 Divide both sides by -5 to isolate x



x=65 Divide





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


So the first part of our answer is: x=65









Since we know that x=65 we can plug it into the equation y=-x%2B80 (remember we previously solved for y in the first equation).



y=-x%2B80 Start with the equation where y was previously isolated.


y=-%2865%29%2B80 Plug in x=65


y=-65%2B80 Multiply


y=15 Combine like terms



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


So the second part of our answer is: y=15









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

So our answers are:

x=65 and y=15

which form the ordered pair