If α+β+γ=0, the line 3αx+βy+2γ=0 passes through the fixed point

The given line is  3αx+βy+2γ=0⇒3αx+βy+2-α-β=0∵α+β+γ=0⇒α3x-2+βy-2=0⇒the given line passes through the point of intersection of the lines 3x – 2 = 0 and y – 2 = 0 i.e.,23,2 for all values of α and β.