Substitution and Elimination

Question

Can you solve this system of equations in 3 variables? 

 

1a+2b+3c=17

2a-2b+4c=20

4a+1b-4c=-3

Answer 1

The answer is YES, I CAN.

 

I believe that the system determinant has value 34; this being non-zero is sufficient demonstration of the solvability.

(But this observation is beyond the substitution approach.)

 

You can immediately eliminate the variable c by addition of the second & third equations together.

That then suggests that you work with equations 1 & 2 to eliminate c...this can be done by premultiplying the first equation by -4 and the second equation by 3, and then adding these two resulting equations.  Then it's easy to solve for x and y...

 

PROCEED! and DO remember to check your answers in all three original equations.