SOLUTION: How do I solve this system of equations? x+y+4z = 10 x+y+2z = 4 x-4y-8z=-36 Im a little lost because i am not sure what equations to start of with or if the system has infi

Algebra ->  Trigonometry-basics -> SOLUTION: How do I solve this system of equations? x+y+4z = 10 x+y+2z = 4 x-4y-8z=-36 Im a little lost because i am not sure what equations to start of with or if the system has infi      Log On


   

Question 929890: How do I solve this system of equations?
x+y+4z = 10
x+y+2z = 4
x-4y-8z=-36
Im a little lost because i am not sure what equations to start of with or if the system has infinite solutions. Can someone please help?
thank you

Found 2 solutions by ewatrrr, Fombitz:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
x+y+4z = 10
-2(x+y+2z = 4)
+-+x+-+y+=+2
.....
4(x+y+2z = 4)
x-4y-8z=-36
5x++=+-20
x = -4 and y = 2 +-+x+-+y+=+2 ,y+=+4+-2
-4 + 2 + 4z = 10
4z = 12
z = 3
..........
(-4, 2, 3) the solution for this System

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use Cramer's rule.
A=%28matrix%283%2C3%2C%0D%0A1%2C1%2C4%2C%0D%0A1%2C1%2C2%2C%0D%0A1%2C-4%2C-8%29%29
abs%28A%29=-10
Since the determinant is not zero, there is a unique solution.
A%5Bx%5D=%28matrix%283%2C3%2C%0D%0A10%2C1%2C4%2C%0D%0A4%2C1%2C2%2C%0D%0A36%2C-4%2C-8%29%29
abs%28A%5Bx%5D%29=40
A%5By%5D=%28matrix%283%2C3%2C%0D%0A1%2C10%2C4%2C%0D%0A1%2C4%2C2%2C%0D%0A1%2C36%2C-8%29%29
abs%28A%5By%5D%29=-20
A%5Bz%5D=%28matrix%283%2C3%2C%0D%0A1%2C1%2C10%2C%0D%0A1%2C1%2C4%2C%0D%0A1%2C-4%2C36%29%29
abs%28A%5Bz%5D%29=-30
.
.
.
x=abs%28A%5Bx%5D%29%2Fabs%28A%29=%2840%29%2F%28-10%29=-4
.
.
y=%28-20%29%2F%28-10%29=2
.
.
z=abs%28A%5Bz%5D%29%2Fabs%28A%29=%28-30%29%2F%28-10%29=3