Consider the system of linear equations \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}z+{{d}_{1}}=0,\] \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}z+{{d}_{2}}=0,\] \[{{a}_{3}}x+{{b}_{3}}y+{{c}_{3}}z+{{d}_{3}}=0,\] Let us denote by \[\Delta (a,b,c)\] the determinant \[\left| \begin{matrix} {{a}_{1}} & {{b}_{1}} & {{c}_{1}} \\ {{a}_{2}} & {{b}_{2}} & {{c}_{2}} \\ {{a}_{3}} & {{b}_{3}} & {{c}_{3}} \\ \end{matrix} \right|\], if \[\Delta \,(a,b,c)\#0,\] then the value of x in the unique solution of the above equations is

• A. \[\frac{\Delta (b,c,d)}{\Delta (a,b,c)}\]
• B. \[\frac{-\Delta (b,c,d)}{\Delta (a,b,c)}\]
• C. \[\frac{\Delta (a,c,d)}{\Delta (a,b,c)}\]
• D. \[-\frac{\Delta (a,b,d)}{\Delta (a,b,c)}\]