Solution:
Keep in mind ,
Equation of line joining two points (a,b) and (p,q) is given by :
![\frac{q-b}{p-a}=\frac{y-b}{x-a}](https://tex.z-dn.net/?f=%5Cfrac%7Bq-b%7D%7Bp-a%7D%3D%5Cfrac%7By-b%7D%7Bx-a%7D)
Equation of line P which is obtained by joining (- 8,15) and (6, - 12) is given by:
![\frac{y-15}{x+8}=\frac{-12-15}{6+8}\\\\ 14(y-15)=-27(x+8)\\\\ 14 y -210= -27 x - 216\\\\ 27 x+14 y+6=0](https://tex.z-dn.net/?f=%5Cfrac%7By-15%7D%7Bx%2B8%7D%3D%5Cfrac%7B-12-15%7D%7B6%2B8%7D%5C%5C%5C%5C%2014%28y-15%29%3D-27%28x%2B8%29%5C%5C%5C%5C%2014%20y%20-210%3D%20-27%20x%20-%20216%5C%5C%5C%5C%2027%20x%2B14%20y%2B6%3D0)
Equation of line Q which is obtained by joining (4,16) and (-9, 10) is given by:
![\frac{y-16}{x-4}=\frac{16-10}{4+9}\\\\ 13(y-16)=6(x-4)\\\\ 13 y -208= 6 x - 24\\\\ 6 x-13 y+184=0](https://tex.z-dn.net/?f=%5Cfrac%7By-16%7D%7Bx-4%7D%3D%5Cfrac%7B16-10%7D%7B4%2B9%7D%5C%5C%5C%5C%2013%28y-16%29%3D6%28x-4%29%5C%5C%5C%5C%2013%20y%20-208%3D%206%20x%20-%2024%5C%5C%5C%5C%206%20x-13%20y%2B184%3D0)
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.