# System of Equations (Tomato subjective 62)

Problem: Consider the system of equations x + y = 2, ax + y = b. Find conditions on a and b under which
(i) the system has exactly one solution;
(ii) the system has no solution;
(iii) the system has more than one solution.
Solution: x + y = 2, ax + y = b
(i) the system has exactly one solution if two lines intersect each other, that is $${{a} \neq {1}}$$
(ii) no solution if the lines are, that is a = 1 & $${{b} \neq {2}}$$
(iii) the system has more than one solution if the two lines are same, that is a = 1 & b = 2.