"Solving a system involving three unknowns."
3d+e-2f=-14
2d-3e+4f=-23
5d+4e-10f=-13
1st times 3 plus the 2nd ---> 11d -2f = -65
1st time 4, subtract the 3rd -->7d + 2f = -43
add these last two ----> 18d = -108
d = -6
in 7d + 2f = -43
-42 + 2f = -43
2f = -1
f = -1/2
in the 1st:
-18 + e -2(-1/2) = -14
e = 3
check in
2nd: LS = -12 -9 - 2 = -23 = RS
3rd: LS = -30 +12 + 5 = -13 = RS
My answer is correct.
d=-6
e=3
f=-1/2