Solving a linear system of equalities and inequalities

[MarcMush]

here is your simple example with JuMP

using JuMP, Clp

m = Model(Clp.Optimizer)

@variables m begin
     x
     y
     z
end

@constraints m begin
      x + 2y +  3z == 10
     2x + 4y + 10z == 20
     4x +  y +   z <= 10
 end

optimize!(m)

value.((x,y,z)) # (0.0, 5.0, 0.0)