Can you help solve this three variable equation?

Question

I'm very confused on this particular topic..I've asked my teacher several times, and I still don't get it..Could you solve this, and give a thorough explanation please?

E+ F + G = -2
2E - 3F - 4G = 5
3E + 2F + 5G = -17

Answer 1

If you're familiar with elimination method from 2- variable equations, you can do something similar. First decide which variable to eliminate, let's say F..Your first equation has an F and your second has a -3F. So if you multiply your first equation by 3 and add it to the second, F will be eliminated.

3E + 3F + 3G = -6
2E - 3F - 4G = 5
This gives you 5E - G = -1 Hold onto this equation 'til later.

Now take the second and third equations and eliminate THE SAME VARIABLE. Multiply the second equation by 2 and the third by 3.

4E - 6F - 8G = 10
9E + 6F + 15 G = - 51
Adding them together gives you 13E + 7G = -41. Put this equation with the one you held onto.

13E + 7G = -41
5E - G = -1
It looks like G will be easier to eliminate by multiplying the second equation by 7
13E + 7G = -41
35E - 7G = -7

48E = -48
E = -1

Now substitute your answer for E in a two-variable equation to find G.
-35 - 7G = -7
-7G = 28
G = -4

Now that you have E and G, you can substitute them in one of your original equations to find F

Answer 2

Use the 3 x 3 Matrix approach.

Answer 3

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