An underdetermined system is one with fewer equations than unknowns, so we can write this as a matrix equation $Ax = b$ with $A$ a matrix that has fewer rows than columns. This implies that solutions, if they exist, will not be unique. Two ways to see this:
Method 1. If you solve the equation $Ax = b$ by row reducing $A$ into echelon form, you will find that not every column in the echelon form can have a pivot. Therefore, when you write down the general solution, there will be free variables, leading to an infinite number of solutions.
Method 2. Since $A$ has fewer rows than columns, then $A$ is an $m \times n$ matrix with $m < n$. Then $\mathrm{rank}(A) \le m$, and since $\mathrm{rank}(A) + \mathrm{nullity}(A) = n$, then $\mathrm{nullity}(A) = n - \mathrm{rank}(A) \ge n - m > 0$. Therefore the null space of $A$ has dimension greater than $0$, so if $x_p$ is a particular solution to the equation, then any vector of the form $x_p + h$ is also a solution for any $h \in \mathrm{Nul}(A)$, and there are infinitely many choices for $h$.