**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.

*Related*

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