Question

On comparing the ratios

111

222

, ,

a b c

a b c

, find out whether the lines representing

the following pairs of linear equations intersect at a point, are parallel or coincident. Also

write whether they are consistent or inconsistent.

(a) 5x – 3y – 8 = 0 ; 2x – 3y – 5 = 0 (b) x – 3y – 11 = 0 ; 5x + y – 7 = 0



(c) y = 6x – 11 ; y = x – 1 (d) 2x – 3y = – 1 ; 2x + 3y = 7



(e) y = – 3x + 5 ; 5x – 4y = – 8 (f) y = 5x – 7 ; – 3x – 2y = – 12



(g) 4x – 3y = 18 ; 3x + 4y = 7 (h) 5x – 4y + 8 = 0 ; 7x + 6y – 9 = 0

(i) 9x + 3y + 12 = 0 ; 18x + 6y + 24 = 0 (j) 6x – 3y + 10 = 0 ; 2x – y + 9 = 0

(k) 3x + 2y = 5 ; 2x – 3y = 7 (l) 2x – 3y = 8 ; 4x – 6y = 9

(m) 5x – 3y = 11 ; – 10x + 6y = –22 (n)

4

2 8

3

x y  

; 2x + 3y = 12

(o) x + y = 5 ; 2x + 2y = 10 (p) x – y = 8 ; 3x – 3y = 16

(q) 2x + y – 6 = 0 ; 4x – 2y – 4 = 0 (r) 2x – 2y – 2 = 0 ; 4x – 4y – 5 = 0​

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