# 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 :

Question : 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

Solution : The given linear equation is 2x + 3y – 8 = 0

(i) For intersecting lines, we know that

$$a_1\over a_2$$ $$\ne$$ $$b_1\over b_2$$

Any intersecting line may be taken as

5x + 2y – 9 = 0

(ii) For parallel lines, $$a_1\over a_2$$ = $$b_1\over b_2$$ $$\ne$$ $$c_1\over c_2$$

$$\therefore$$ line parallel to 2x + 3y – 8 = 0 may be taken as

6x + 9y + 7 = 0

(iii) For coincident lines, $$a_1\over a_2$$ = $$b_1\over b_2$$ = $$c_1\over c_2$$

Any line coincident to 2x + 3y – 8 = 0 may be taken as

4x + 3y – 16 = 0