The graphs of the linear equations 3x - 2y = 8 and 4x + 3y = 5 intersect at the point P(α, β). What is the value of (2α - β)?

Solution (By Examveda Team)

$$\eqalign{ & 3{x_{ \times 3}} - 2{y_{ \times 3}} = {8_{ \times 2}} \to \left( {\text{i}} \right) \cr & \underline {4{x_{ \times 2}} + 3{y_{ \times 2}} = {5_{ \times 2}}} \to \left( {{\text{ii}}} \right) \cr & 17x = 34 \cr & x = 2 \cr & y = - 1 \cr & \left( {2\alpha - \beta } \right) = \left\{ {2\left( 2 \right) - \left( { - 1} \right)} \right\} = 4 + 1 = 5 \cr} $$