The graphs of the equations 2x + 3y = 11 and x - 2y + 12 = 0 intersects at P(x₁, y₁) and the graph of the equation x - 2y + 12 = 0 intersects the x-axis at Q(x₂, y₂). What is the value of (x₁ - x₂ + y₁ + y₂)?

Solution (By Examveda Team)

$$\eqalign{ & 2x + 3y = 11{\text{ }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}\left( {\text{i}} \right) \cr & x - 2y = - 12{\text{ }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\left( {{\text{ii}}} \right)_{ \times 2}} \cr & \,2x - 4y = - 24 \cr & \underline {\,2x + 3y = 11\,} \cr & \,\,\,\,\,\,\,\,\,\,\,\,7y = 35 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,y = 5 \cr & {\text{From equation}}\left( {\text{i}} \right) \cr & 2x + 15 = 11 \cr & x = - 2 \cr & \left( {{x_1},\,{y_1}} \right) = \left( { - 2,\,5} \right) \cr & {\text{At }}x{\text{ - axis}},\,y = 0 \cr & x - 2 \times 0 = - 12 \cr & x = - 12 \cr & \left( {{x_2},\,{y_2}} \right) = \left( { - 12,\,0} \right) \cr & {x_1} - {x_2} + {y_1} + {y_2} = - 2 + 12 + 5 + 0 = 15 \cr} $$