SOLUTION: solve the system use the substitution method 2x-y-z=15 4x+5y+2z=10 -x-4y+3z=-20 please help don't understand it

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Question 110553: solve the system use the substitution method
2x-y-z=15
4x+5y+2z=10
-x-4y+3z=-20
please help don't understand it
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
solve the system use the substitution method
:
Eq1: 2x - y - z = 1
Eq2: 4x +5y +2z = 10
Eq3: -x- 4y +3z =-20
:
Not sure why you would want to use the substitution method here. Elimination makes sense. But let's try to substitute and see what happens;
Using eq1:
2x - y - z = 1
-y = 1 - 2x + z
y = 2x - z - 1; make y positive multiply by -1
:
Substitute (2x-z-1) for y in Eq2
4x + 5(2x-z-1) + 2z = 10
4x + 10x - 5z - 5 + 2z = 10
14x - 3z = 10 + 5
14x - 3z = 15
-3z = -14x + 15
3z = 14x - 15
z = 14%2F3x - 5
:
Substitute (2x-z-1) for y in Eq3
-x - 4(2x-z-1) + 3z = -20
-x - 8x + 4z + 4 + 3z = -20
-9x + 7z = -20 - 4
-9x + 7z = -24
:
Substitute (14%2F3x-5) for z in the above equation
-9x + 7(14%2F3x-5) = -24
-9x + 98%2F3x - 35 = - 24
-27%2F3x + 98%2F3x = - 24 + 35
71%2F3x = 11
x = 11*3%2F71
x = 33%2F71
x = .46478; not even an integer, disgusting!
:
Using -9x + 7z = -24, substitute for x and find z:
-9(.46478) + 7z = -24
7z = -24 + 4.1831
z = -19.8169/7
z = -2.8309
:
Find y using y = 2x - z - 1
y = 2(.46478) - (-2.8309) -1
y + .92956 + 2.8309 - 1
y = 2.76056
:
All these solutions check out on the Ti83 Matrix function. Really a nasty problem, hope this helped you out.