What would be the simplest way to eliminate one of the variables? Below is a system of three equations in three variables:

Question

1. x+y+3z=7
2. 2x-4y+z=7
3. 3x+5y-4z=-6

Answer 1

one simple way is to substitute x #1 into #2 and #3:

2(7-y-3z) - 4y + z = 7
3(7-y-3z) + 5y - 4z = -6
which gives you

-6y -5z = -7
2y - 13z = -27

now we see 2y = 13z-27, so

-3(13z-27) - 5z = -7
-44z = -88
z = 2

so, y = (26-27)/2 = -1/2
and x = 7-(-1/2)-6 = 1/2