The two lines, P and Q, are graphed below: Line P is drawn by joining ordered pairs negative 8,15 and 6, negative 12. Line Q is drawn by joining ordered pairs 4,16 and negative 9,10 Determine the solution and the reasoning that justifies the solution to the systems of equations

Solution:Keep in mind , Equation of line joining two points (a,b) and (p,q) is given by :      [tex]\frac{q-b}{p-a}=\frac{y-b}{x-a}[/tex]Equation of line P which is obtained by  joining  (- 8,15) and (6, - 12) is given by:  [tex]\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[/tex]Equation of line Q which is obtained by  joining  (4,16) and (-9, 10) is given by:  [tex]\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[/tex]Equation of line P and Q are 27 x+14 y+6=0-------(1)× 2 6 x-13 y+184=0-------(2)× 954 x + 2 8 y+12=0---(1)54 x -117 y +1656=0----(2)(1) - (2)145 y= 1644y=11.33,27 x+14 y+6=0-------(1)×136 x-13 y+184=0-------(1)×14351 x + 182 y + 78=0-----(1)84 x - 182 y +2576=0----(2)(1) + (2)435 x + 2654=0x = - 6.11So, solution set is (-6.11, 11.33)Option (C) is true. (−2, 4), because this point makes both the equations incorrect.