consider line X.
(-3, 12), (7, -16) are 21 points on this line, so by the 2-point form of the equation of a line, the equation of X is given as follows:
[tex] \frac{12-(-16)}{-3-7}= \frac{y-12}{x-(-3)} [/tex]
[tex]\frac{28}{-10}= \frac{y-12}{x+3} [/tex]
[tex]28(x+3)=-10(y-12)[/tex]
[tex]28x+84=-10y+120[/tex]
[tex]28x+10y-36=0[/tex], divide by 2 to simplify:
[tex]14x+5y-18=0[/tex]
similarly, the equation of Y is found using the points (0, -14) and (11, 8):
[tex] \frac{-14-8}{0-11}= \frac{y-(-14)}{x-0} [/tex]
[tex] \frac{-22}{-11}= \frac{y+14}{x} [/tex]
[tex]2= \frac{y+14}{x} [/tex]
[tex]2x-y-14=0[/tex]
so y=2x-14,
substitute y=2x-14 in 14x+5y-18=0:
14x+5y-18=0
14x+5(2x-14)-18=0
14x+10x-70-18=0
24x=88
x=3.667, then y=2x-14=2*3.667-14=-6.66
the intersection point is (3.667, -6.66), it is the only point which satisfies the equations of the lines, that were found.
Answer: (4, −6), because this point makes both the equations true
