SOLUTION: What is 2x-y+z=14
-x+2y-4z=5
x+4y-6z=-1
This is solve the system using the elimination method get the x,y, and z please help this is hard.
Algebra.Com
Question 228736: What is 2x-y+z=14
-x+2y-4z=5
x+4y-6z=-1
This is solve the system using the elimination method get the x,y, and z please help this is hard.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
2x - y + z = 14
-x+ 2y -4z = 5
x + 4y -6z =-1
:
You're right this is a pain!
:
Add the 2nd and 3rd equations, to eliminate x
-x+ 2y -4z = 5
x + 4y -6z =-1
-----------------adding eliminates x
0 + 6y - 10z = 4
Simplify, divide by 2
3y - 5z = 2
:
Multiply the 2nd equation by 2 and add to the 1st equation
2x - y + z = 14
-2x+ 4y -8z = 10
-----------------addition eliminates x again
0 + 3y - 7z = 24
:
Two 2 unknown equation to deal with now
:
Subtract 3y - 5z = 2 from the above equation
3y - 7z = 24
3y - 5z = 2
---------------subtraction eliminates y, find z
0 - 2z = 22
-2z = 22
z =
z = -11
:
find y using the equation 3y - 5z = 2
3y - 5(-11) = 2
3y + 55 = 2
3y = 2 - 55
3y = -53
y =
y = -17.667
:
Find x using the 1st equation 2x - y + z = 14
2x - (-17) - 11 = 14
2x + 17 - 11 = 14
2x + 6 = 14
2x = 14 - 6.667; go to decimals here
2x = 7.333
x = 3.667
;
:
It's kind of disgusting they give you a problem that doesn't have integer solutions.
I checked this using the matrix feature on my TI83, so I think it's right
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