Systems of Linear Equations with 3 Variables: Substitution

Consider the following system of three linear equations with three variables $(x,y,z)$.

\begin{align} 2x+3&y+z = 10 \ 3x + 2&y + 3z = 10 \ ax + b&y + cz = 10

\end{align}

where $a,b,c$ are constants. Which of the following values of $a,b,c$ results in an infinite number of solutions to the above system of equations? (The answer choice $(3,4,5)$ means $a=3, b=4, c=5$).