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

Solution (By Examveda Team)

$$\eqalign{ & 3x + y = 5 \cr & \underline {2x - y = 5} \cr & 5x = 10 \cr & x = 2,\,y = - 1 \cr & \left( {\alpha ,\,\beta } \right) = \left( {2,\, - 1} \right) \cr & 3\alpha + \beta = 3 \times 2 - 1 = 5 \cr} $$