The graph of the equations 5x - 2y + 1 = 0 and 4y - 3x + 5 = 0, intersect at the point P(α, β). What is the value of (2α - 3β)?

Solution (By Examveda Team)

$$\eqalign{ & 5x - 2y = - 1\,.\,.\,.\,.\,.\,.\,.\,\left( {\text{i}} \right) \times 2 \cr & 4y - 3x = - 5\,.\,.\,.\,.\,.\,.\,.\,\left( {{\text{ii}}} \right) \cr & 10x - 4y = - 2 \cr & \underline {\, - 3x + 4y = - 5\,} \cr & 7x = - 7 \cr & x = - 1,\,\,y = - 2 \cr & 2\alpha - 3\beta \cr & = 2\left( { - 1} \right) - 3\left( { - 2} \right) \cr & = - 2 + 6 \cr & = 4 \cr} $$