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.

Guest Mar 29, 2017

#3**0 **

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 }

CPhill
Mar 29, 2017