solve 6a+6b-c=-2, 8a+4b+c=-7, 2a-6b-7c=10 by elimination

Question

its one problem but three equations. i never can do these stupid things correct. please help

Answer 1

From the first equation, c=6a+6b+2, which can be substituted in both of the other equations:

8a+4b+6a+6b+2=-7; 14a+10b=-9;

2a-6b-42a-42b-14=10; -40a-48b=24; 5a+6b=-3.

Take these two equations and multiply the first by 3 and the second by 5:

42a+30b=-27; 25a+30b=-15 so 30b=-15-25a (6b=-3-5a). Now substitute for 30b in the other equation:

42a-15-25a=-27; 17a=-12, a=-12/17. 6b=-3+60/17=9/17; b=3/34

c=-(7+8a+4b)=-(7-96/17+6/17)=-(1/17)(119-96+6)=-29/17.

To check this solution, substitute for a, b and c in the original equations.

Solution: a=-12/17, b=3/34, c=-29/17.