How to solve this system of equations 4 x + 2 y + 4 z = 0 2

Lydia Carey

Lydia Carey

Answered question

2022-06-13

How to solve this system of equations
4 x + 2 y + 4 z = 0
2 x + y + 2 z = 0
4 x + 2 y + 4 z = 0

Answer & Explanation

Blaine Foster

Blaine Foster

Beginner2022-06-14Added 33 answers

Note that your system of equations is actually a single equation in various avatars. (i.e.) one is scalar multiple of the other. Put another way, these equations convey the same information, nothing new!
4 x + 2 y + 4 z = 0 2 ( 2 x + y + 2 z = 0 ) 4 x + 2 y + 4 z = 0
Since there are three unknowns, and only one equations, two parameters are required to fix a solution. We can have a parametric solution as follows:
Set x = λ and y = μ. Then,
2 λ + μ + 2 z = 0 z = 2 λ μ 2
Hence, the triplet ( λ , μ , 2 λ μ 2 ) with λ , μ R is a solution to your system.

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