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# Given the linear equation $$2x + 3y – 8 = 0$$, write another linear equation in two variables such that the geometrical representation of the pair so formed is: (i) Intersecting lines(ii)Parallel lines(iii)Coincident lines

Ans.(i) Intersecting lines

The condition for intersecting lines is :
$${{a_1}\over {a_2}} \ne {{b_1}\over {b_2}}$$

So the second equation can be $$x + 2y = 3$$

Since, $${{a_1}\over {a_2}} \ne {{b_1}\over {b_2}}$$
=>$${{2}\over {1}} \ne {{3}\over {2}}$$

(ii) Parallel lines

The condition for parallel lines is :

$${{a_1}\over {a_2}} = {{b_1}\over {b_2}} \ne {{c_1}\over {c_2}}$$

So the second equation can be $$2x + 3y – 2 = 0$$

Since, $${{a_1}\over {a_2}} = {{b_1}\over {b_2}} \ne {{c_1}\over {c_2}}$$
=>$${{2}\over {2}} = {{3}\over {3}} \ne {{-8}\over {-2}}$$

(ii) Coincident lines

The condition for coincident lines is :

$${{a_1}\over {a_2}} = {{b_1}\over {b_2}} \ne {{c_1}\over {c_2}}$$

So the second equation can be $$4x + 6y – 16 = 0$$
Since, $${{a_1}\over {a_2}} = {{b_1}\over {b_2}} = {{c_1}\over {c_2}}$$
=>$${{2}\over {4}} = {{3}\over {6}} = {{-8}\over {-16}}$$
=>$${{1}\over {2}} = {{1}\over {2}} = {{1}\over {2}}$$