Question 682221: Hello I have to solve three equations with three variables
The equations are
6q-r+2s=8
2q+3r-s=-9
4q+2r+5s=1
I have the equations using the process of elimination to find x y and z
The problem is I've been on this question for more than an hour either getting decimals as my answers and or equations which I can't solve
Honestly I don't know what I'm doing wrong.Ive tried to eliminate the q's first but afterwards towards solving I got 2.5 which I know is wrong
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 6q - r + 2s = 8
2q + 3r - s = -9
4q + 2r + 5s= 1
:
There are several ways to do this, sometimes it's helpful to slip "substitution" among the eliminations.
:
Multiply 1st eq by -1 and add to the other 2
-6q + r - 2s = -8
2q + 3r - s = -9
4q + 2r + 5s = 1
-------------------Adding eliminates q
6r + 2s = -16
Simplify, divide by 2
3r + s = -8
s = -3r - 8
:
Taking the last two equations, multiply the middle equation by 2
4q + 6r - 2s = -18
4q + 2r + 5s = 1
---------------------Subtraction eliminates q
4r - 7s = -19
replace s with (-3r-8)
4r -7(-3r-8) = -19
4r + 21r + 56 = -19
25r = -19 - 56
25r = -75
r = -75/25
r = -3
:
Find s
s = -3(-3) - 8
s = 9 - 8
s = 1
:
Find q using the first equation
6q -r + 2s = 8,
replace r and s
6q -(-3) + 2(1) = 8
6q + 3 + 2 = 8
6q = 8 - 5
6q = 3
q = 3/6
q = .5 or 1/2
:
:
You can confirm this in the original equations
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