SOLUTION: I am doing solving systems by elimination I need help knowing the process of how to do it. here is an example: 7b-5c=11 -4c-2b=-14

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Question 265033: I am doing solving systems by elimination
I need help knowing the process of how to do it.
here is an example:
7b-5c=11
-4c-2b=-14
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
I am doing solving systems by elimination
I need help knowing the process of how to do it.
here is an example:
7b-5c=11
-4c-2b=-14
--------------------
Procedure:
1st: Decide which variable you want to eliminate:
2nd: Decide if you are going to add or subtract to eliminate that variable:
OK
Let's eliminate "b" by adding.
Multiply the 1st equation by 4
Multiply the 2nd quation by 7
You get:
28b - 20c = 4*11
-28b- 14c = 7*-14
----------------------------
Add and the "b" terms will disappear:
-34c = 4*11 -7*14
-34c = -54
c = 27/17
-------
Substitute into one of the original equation to solve for "b":
7b-5c=11
7b - 5(27/17) = 11
7b = 187/17 + 135/17
7b = 322/17
b = 46/17
=================
Cheers,
Stan H.

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

 7b - 5c =  11
-4c - 2b = -14

Let's switch the order of terms on the left of the
second equations, so that like letters line up.

 7b - 5c =  11
-2b - 4c = -14

See the 7 and the -2 coefficients of b?  We want to multiply
both equations through by numbers that will make the coefficients
of b become equal in absolute value but opposite in sign.

7 and -2 are already opposite in sign, so we need to make them equal
in absolute value.

To do this we look at their absolute values, 7 and 2.
Now 7 and 2 have a least common multiple of 14. So we
multiply the first equation by 2 and multiply the second 
equation through by 7:

 14b - 10c =  22
-14b - 28c = -98

Now we draw a line under the pair of equations 
and add them term by term:

 14b - 10c =  22
-14b - 28c = -98
----------------
  0  - 38c = -76
      -38c = -76
         c = 2

Return to the original two equations:

 7b - 5c =  11
-2b - 4c = -14

See the -5 and the -4 coefficients of c?  We want to multiply
both equations through by numbers that will make the coefficients
of c become equal in absolute value but opposite in sign.

-5 and -4 are not opposite in sign, so we will need to multiply
one of them through by a positive number and the other through by
a negative number to make them opposite in sign.

We need to make them equal in absolute value. To do this we look 
at their absolute values, 5 and 4. Now 5 and 4 have a least common 
multiple of 20. So we multiply the first equation by 4 and multiply 
the second equation through by -5:

28b - 20c = 44
10b + 20c = 70

Now we draw a line under the pair of equations 
and add them term by term:

28b - 20c =  44
10b + 20c =  70
----------------
38b +  0  = 114
      38b = 114
        b = 3

We found BOTH letters by elimination.  Sometimes
people only find one variable by the elimination method,
and then switch over to the substitution method to find 
the other variable.  Either way is correct.

Edwin