Triangular linear equation set solver

--task? create an algorithm capaple of solving triangular linear equation sets.
--arguments are n(size of the matrix), matrix(the matrix containing the values) and results(the results of each line of the matrix)

--for example, the linear equation set{x+y+z=-1, y+z=2,z=3} would be represented as 3,{{1,1,1},{0,1,1},{0,0,1}},{1,2,3} and the solution {-1,-1,3}

function solve(n,matrix,results)
--n is pretty much redundant and can be replaced with #matrix, but the assignment nazis still require it
--you can probably uncomment this and maybe remove n from arguments.
--n=#matrix

    local vars={}
--initializing vars
    for i=1,n do
        vars[i]=0
    end

--get
    if matrix[#matrix][1]==0 then
    --normal triangular matrix
        for i=1,n do
        --removing through substitution already known values
            for j=1,n do
            results[i]=(results[i]-(vars[j]*matrix[i][j]))
            end
        vars[i]=(results[i]/matrix[i][j])
        end
    else
    --inverted triangular matrix
        for i=n,1,-1 do
        --i could do this by passing different args for the for loop, but i'm too lazy for that atm
            for j=1,n do
            results[i]=(results[i]-(vars[j]*matrix[i][j]))
            end
        vars[i]=(results[i]/matrix[i][j])
        end

    end

return vars
end


--example test case

local a,b,c=3,{{1,1,1},{0,1,1},{0,0,1}},{1,2,3}

print(unpack(solve(a,b,c)))