The lines 2x + y = 5 and x + 2y = 4 intersect at the point?

Solution (By Examveda Team)

$$\eqalign{ & 2x + y = 5..............(i) \cr & x + 2y = 4..............(ii) \cr & {\text{Multiply equation (ii) by 2}} \cr & 2x + 4y = 8............(iii) \cr} $$
Now subtracting equation (i) from (iii)
$$\eqalign{ & {\text{ }}2x + 4y = 8 \cr & \mathop {}\limits_ - 2x\mathop + \limits_ - \,\,y\, = 5 \cr & \overline {\underline {\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3y = 3{\text{ }}} } \cr & y = 1 \cr & x = 2 \cr & \therefore {\text{Intersection point = }}\left( {2,1} \right) \cr} $$