SOLUTION: Can you help me with the following question? Solve each system by elimination. Check your answers. #4 {a+b+c=-3 { 3b-c=4 {2a-b-2c=-5

Question 162132: Can you help me with the following question?
Solve each system by elimination. Check your answers. #4
{a+b+c=-3
{ 3b-c=4
{2a-b-2c=-5
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
line the equations up by putting 0 for the missing variables:
:
a + b + c = -3
0 +3b - c = +4
2a -b -2c = -5
:
Add equations 1 and 3:
a + b + c = -3
2a -b -2c = -5
------------------addition eliminates b
3a - c = -8
:
Multiply equation 3 by 3 and and add to equation 2
0 +3b - c = +4
6a-3b -6c = -15
-------------------addition eliminates b again
6a - 7c = -11
:
We have two 2 unknown equations now
3a - c = - 8
6a - 7c = -11
:
Multiply the 1st equation by 2, subtract the 2nd equation:
6a - 2c = -16
6a - 7c = -11
-----------------subtraction eliminates a, find c
0a + 5c = -5
c =
c = -1
:
Use the 1st two unknown equation to find a
3a - c = - 8
3a - (-1) = -8
3a + 1 = -8
3a = -8 - 1
3a = -9
a =
a = -3
:
We can find b using the 2nd original equation:
3b - c = 4
3b -(-1) = 4
3b + 1 = 4
3b = 4 - 1
3b = 3
b = +1
:
Check solutions in the original 1st equation
a + b + c = -3
-3 + 1 - 1 = -3
:
Was all this understandable, any questions?
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