Solution:

Keep in mind ,

Equation of line joining two points (a,b) and (p,q) is given by :

Equation of line P which is obtained by joining (- 8,15) and (6, - 12) is given by:

Equation of line Q which is obtained by joining (4,16) and (-9, 10) is given by:

Equation of line P and Q are

27 x+14 y+6=0-------(1)× 2

6 x-13 y+184=0-------(2)× 9

54 x + 2 8 y+12=0---(1)

54 x -117 y +1656=0----(2)

(1) - (2)

145 y= 1644

y=11.33,

27 x+14 y+6=0-------(1)×13

6 x-13 y+184=0-------(1)×14

351 x + 182 y + 78=0-----(1)

84 x - 182 y +2576=0----(2)

(1) + (2)

435 x + 2654=0

x = - 6.11

**So, solution set is (-6.11, 11.33)**

**Option (C) is true. (−2, 4), because this point makes both the equations incorrect.**