Hey guys,
I would greatly appreciate if any one of you maths geniuses could help me with this simultaneous equation question.
The question itself seems very unusual in that I don't end up getting real values for the variables x, y and z.
The question is:
x + 5y + 3z = -1
3x + 17y + 5z = 1
2x + 11y + 4z = 0
Again, any kind of help would be greatly appreciated.
Thanks.
James.
+128408 x + 5y + 3z = -1
3x + 17y + 5z = 1
2x + 11y + 4z = 0
Multiply the first equation by -3 = -3x - 15y - 9z = 3.......add this to the second
2y - 4z = 4 → y - 2z = 2 (1)
Multiply the first equation by -2 = -2x - 10y-6z = 2.....add this to the third
y -2z = 2 (2)
Now....since (1) and (2) are exactly the same, we will have infinite solutions for this system
Holding z constant and using (2)
y = 2z + 2
And using the first equation
x + 5 (2z + 2) + 5z = -1
x + 10z + 10 + 5z = -1
x + 15z + 10 = -1
x = -11 - 15z
So......one form of the solution is {x, y , z } = { -11-15z, 2z + 2, z }
