Consider the following system of three linear equations in two variables:
MATHEMATICS · Multi-part · CBSE · Mathematics · Pair of Linear Equations in Two Variables · Pair of Linear Equations in Two Variables
Problem
Consider the following system of three linear equations in two variables:
(i) Examine every possible pair of equations from the above set and classify the two lines involved as coincident, parallel, or intersecting. Show your working clearly.
(ii) Using the results of part (i), decide whether the complete system of three equations has no solution, exactly one solution, or infinitely many solutions. Give reasons for your answer with reference to the possible graphs of the lines.
(iii) If a unique solution exists, find it algebraically. If not, explain why an algebraic solution is impossible or not unique in this case.