4e+4f+g=24 2e-4f+g=0 5e-4f-5g=12

Question

Find the variables in the equations.

Answer 1

start with the first two equations and add them together

4e + 4f + g = 24

2e - 4f + g = 0

add and get 6e + 2g = 24  (set this aside)

add the 1st and 3rd equation

4e + 4f + g = 24

5e - 4f - 5g = 12

add them and get 9e - 4g = 36 (set this aside)

now, take the first equation and multiply it by 2

12e +4g = 48

add this to 9e - 4g = 36 and get

21e = 84     divide both sides by 21 and e = 4

now work backwards to find g and f

9(4) - 4g = 36

36 - 4g = 36

-4g = 0 so g= 0

now find f

4(4) + 4f + 0 = 24

16 + 4f = 24

4f = 8 so f = 2

final answer is e = 4, f= 2 and g = 0