SOLUTION: i need help doing this problem: -3a + b = 4 -9a + 5b = -1 need this answered tonight!!! thank you!! (this is a really neat place!!)

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Question 175480: i need help doing this problem:
-3a + b = 4
-9a + 5b = -1
need this answered tonight!!! thank you!!
(this is a really neat place!!)
Found 2 solutions by jim_thompson5910, Mathtut:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:
system%28-3a%2Bb=4%2C-9a%2B5b=-1%29


-3%28-3a%2Bb%29=-3%284%29 Multiply the both sides of the first equation by -3.


9a-3b=-12 Distribute and multiply.


So we have the new system of equations:
system%289a-3b=-12%2C-9a%2B5b=-1%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%289a-3b%29%2B%28-9a%2B5b%29=%28-12%29%2B%28-1%29


%289a%2B-9a%29%2B%28-3b%2B5b%29=-12%2B-1 Group like terms.


0a%2B2b=-13 Combine like terms. Notice how the x terms cancel out.


2b=-13 Simplify.


b=%28-13%29%2F%282%29 Divide both sides by 2 to isolate b.


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


9a-3b=-12 Now go back to the first equation.


9a-3%28-13%2F2%29=-12 Plug in b=-13%2F2.


9a%2B39%2F2=-12 Multiply.


2%289a%2B39%2Fcross%282%29%29=2%28-12%29 Multiply both sides by the LCD 2 to clear any fractions.


18a%2B39=-24 Distribute and multiply.


18a=-24-39 Subtract 39 from both sides.


18a=-63 Combine like terms on the right side.


a=%28-63%29%2F%2818%29 Divide both sides by 18 to isolate a.


a=-7%2F2 Reduce.


So our answer is a=-7%2F2 and b=-13%2F2.


Which form the ordered pair .


This means that the system is consistent and independent.

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
this is a system of equation that we will solve similtaneously
:
-3a + b = 4 ....eq 1
-9a + 5b = -1...eq 2
:
multiply eq 1 by -3
:
9a-3b=-12....revised eq 1
-9a+5b=-1....eq 2
:
I lined the 2 equations up so you can see that when we add the equations together the a terms are eliminated because 9a-9a=0. We are left with
-3b+5b=-12-1.
:
2b=-13
:
highlight%28b=-13%2F2%29
:
now take b's found value and plug it back into either equation. I will use eq 1
:
-3a + (-13/2)=4 ........now multiply all terms by 2 to get rid of fraction
:
-6a-13=8
:
-6a=21
:
highlight%28a=-21%2F6=-7%2F2%29