# Thread: Simultaneous equations

1. ## Simultaneous equations

I have:

2x-y+3z = 4
x+y+az = 3
x+ay+z = 3

and I'm wondering what the easiest way to solve out a is, cause i've been trying and it just ends up looking worse than it did before i started out.. ^^

2. Originally Posted by weasley74
I have:

2x-y+3z = 4
x+y+az = 3
x+ay+z = 3

and I'm wondering what the easiest way to solve out a is, cause i've been trying and it just ends up looking worse than it did before i started out.. ^^
What are you trying to find? if a=0 or a=1 the system is degenerate (reduces
to two independent equations) and so has multiple solutions, any other
value of a will allow a unique solution for x, y and z in terms of a.

RonL

3. Originally Posted by CaptainBlack
What are you trying to find? if a=0 or a=1 the system is degenerate (reduces
to two independent equations) and so has multiple solutions, any other
value of a will allow a unique solution for x, y and z in terms of a.

RonL
I think the system will have no solution for a = 0 ......

2x - y + 3z = 4 ..... (1)
x + y = 3 .... (2)
x + z = 3 ..... (3)

(1) + (2): 3x + 3z = 7 => x + z = 7/3 is inconsistent with (3).

4. Originally Posted by mr fantastic
I think the system will have no solution for a = 0 ......

2x - y + 3z = 4 ..... (1)
x + y = 3 .... (2)
x + z = 3 ..... (3)

(1) + (2): 3x + 3z = 7 => x + z = 7/3 is inconsistent with (3).
Yup, made a mistake when examining that case

RonL