# Solving system of equations
**URL:** https://discourse.julialang.org/t/solving-system-of-equations/27691
**Category:** New to Julia
**Created:** [August 18, 2019, 7:42pm UTC](https://discourse.julialang.org/t/solving-system-of-equations/27691 "2019-08-18T19:42:19Z")
**Posts on this page:** 4
**Page:** 1
### Author:  [@zaccazy](https://discourse.julialang.org/u/zaccazy)
#### Post date: [August 18, 2019, 7:42pm UTC](https://discourse.julialang.org/t/solving-system-of-equations/27691/1 "2019-08-18T19:42:19Z")
Hi. I’m interested in ‘nlsolve’ function for solving system of equations.
Let us consider simple example:
Eq.1: y=a+x
Eq.2: y=2x-1,
where a is a vector that it can take values 3 and 5.
I want to solve system of equations for each value of a.
For a=3, (x,y)=(4,7), and for a=5, (x,y)=(6,11).
I solve it in a loop:
using NLsolve
function f!(F, x, a)
F[1] =a+x[1]-x[2]
F[2] =2\*x[1]-1-x[2]
end
K=zeros(2, length(a))
initial\_x=[0.1; 0.2]
a=[3.0; 5.0]
for i=1:length(a)
res=nlsolve((F,x) → f!(F, x, a[i]), initial\_x)
K[:,i]=res.zero
end
Is there any smart way to avoid looping?
Also, I would appreciate if you can explain the helper function `n_ary`.
Thank you.
---
### Author:  [@kristoffer.carlsson](https://discourse.julialang.org/u/kristoffer.carlsson)
#### Post date: [August 18, 2019, 9:17pm UTC](https://discourse.julialang.org/t/solving-system-of-equations/27691/2 "2019-08-18T21:17:03Z")
This is just a system of linear equations so there is no need for NLSolve. Assuming it is just a simple example, what is wrong with writing a loop?
---
### Author:  [@kevbonham](https://discourse.julialang.org/u/kevbonham)
#### Post date: [August 19, 2019, 12:32am UTC](https://discourse.julialang.org/t/solving-system-of-equations/27691/3 "2019-08-19T00:32:58Z")
Welcome to the Julia community! I can’t help with your particular issue, but it might be worth taking a look at [this thread](https://discourse.julialang.org/t/psa-make-it-easier-to-help-you/14757) about posting questions here in discourse. In particular, you can get the code formatted, making it a bit easier to read. Compare
function foo()
println(“this looks like normal text”)
end
To:
```julia
function bar()
println("oh, so much better!")
end
```
---
### Author:  [@nilshg](https://discourse.julialang.org/u/nilshg)
#### Post date: [August 20, 2019, 9:43am UTC](https://discourse.julialang.org/t/solving-system-of-equations/27691/4 "2019-08-20T09:43:50Z")
If it’s just about avoiding this loop:
> [@zaccazy](#):
>
> ```julia
> a=[3.0; 5.0]
>
> for i = 1:length(a)
> res = nlsolve((F,x) -> f!(F, x, a[i]), initial_x)
> K[:,i] = res.zero
> end
>
> ```
then I guess you could do
```julia
res = [nlsolve((F,x) -> f!(F, x, aᵢ), initial_x) for aᵢ in a]
K = [r.zero for r in res]
```
But I’m not sure that’s an improvement over the loop? Loops in Julia are generally as fast as “vectorized” code, so in case you’re coming from Matlab/R or a similar environment where vectorization is the key to fast code you can stop worrying!