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!!)

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) (Show Source): You can put this solution on YOUR website!

Start with the given system of equations:

Multiply the both sides of the first equation by -3.

Distribute and multiply.

So we have the new system of equations:

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

Group like terms.

Combine like terms. Notice how the x terms cancel out.

Simplify.

Divide both sides by to isolate .

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

Now go back to the first equation.

Plug in .

Multiply.

Multiply both sides by the LCD to clear any fractions.

Distribute and multiply.

Subtract from both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

So our answer is and .

Which form the ordered pair .

This means that the system is consistent and independent.

Answer by Mathtut(3670) (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
:

:
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
:

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