A point with positive coordinates is common to all three curves given below:

MATHEMATICS · Multi-part · CBSE · Mathematics · Pair of Linear Equations in Two Variables · Pair of Linear Equations in Two Variables

Problem

A point

P

with positive coordinates is common to all three curves given below: (i) Determine the coordinates of

P

by solving the three equations simultaneously. (ii) Hence, find the value of the parameter

a

. (iii) Investigate algebraically whether any real point other than

P

can satisfy all three equations at the same time.