I've had a little break in solving systems of equations and so I wanted to verify here that my own answer to this problem is 100% correct and done :) So I have the following problem:
Solve the system of equations:
Because this is an underdetermined system we will have infinite amount of solutions. I will solve $x_1$ and $x_2$ explicitly in terms of $x_3$ and $x_4$. By multiplying the first equation by $3$ and adding it to the second we get:
By substituting $x_2$ into the first equation we get:
From which we get
So the solution is:
where $x_3,x_4$ are free variables.