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we start by making c the subject of the first equation

c=6-a-b

we substitute this value of c into the other equations

2a-b+(6-a-b)=3 => a-2b=-3 .....4

3a-b+(6-a-b)=4 => 2a-2b=-2 .....5

making a the subject of equation 4;

a=2b-3

substituting a into equation 5;

2(2b-3)-2b =-2 => 2b=4

b=2

a=2b-3; a=2(2)-3;

a=1

a+b+c =6

1+2+c=6 => c=6-3

c=3

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