Question

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. (0, 8), because this point is true for both the equations (0, 8), because the lines intersect the y-axis at these points (−2, 4), because this point makes both the equations incorrect (−2, 4), because it is the point of intersection of the two graphs

Answer 1

Solution:

Keep in mind ,

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

     $\frac{q-b}{p-a}=\frac{y-b}{x-a}$

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

$\frac{y-15}{x+8}=\frac{-12-15}{6+8}\\\\ 14(y-15)=-27(x+8)\\\\ 14 y -210= -27 x - 216\\\\ 27 x+14 y+6=0$

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

$\frac{y-16}{x-4}=\frac{16-10}{4+9}\\\\ 13(y-16)=6(x-4)\\\\ 13 y -208= 6 x - 24\\\\ 6 x-13 y+184=0$

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.