Question 1009091
You made the correct system of equations, {{{system(a-b+c=-2,a+b+c=-4,4a+2b+c=4)}}}.


Next, choose either row-reduction matrix operations; or elimination method, or substitution method.


Substitution method is the least advanced way, and as a start, take E1, solve for c:
{{{a-b+c=-2}}}
{{{c=-a+b-2}}}
{{{c=b-a-2}}}
and substitute into E2 and E3:
{{{system(a+b+b-a-2=-4,4a+2b+b-a-2=4)}}}
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{{{system(2b-2=-4,3a+3b-2=4)}}}
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{{{system(2b=-2,3a+3b=6)}}}
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{{{system(b=-1,a+b=2)}}}, which shows one of the coefficients, easily allowing for finding another by using that other's now known value...
{{{a=2-b}}}
{{{a=2-(-1)}}}
{{{a=2+1}}}
{{{highlight(a=3)}}}, and obviously just found as well, {{{highlight(b=-1)}}}.


You still want to find the value for c.  Use any equation of the system that you want.