Row Reduction & Rank · Hard problem

A $3$-good market model gives the equilibrium system $x+2y+3z=p_1$, $2x+5y+tz=p_2$, $x+3y+4z=p_3$, where $t$ is a tax-policy parameter. For which value of $t$ does this system fail to have a unique equilibrium (the coefficient matrix becomes singular) for every price vector $(p_1,p_2,p_3)$?