Question 162132
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 = {{{(-5)/5}}}
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 = {{{(-9)/3}}}
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?