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:
![\frac{12-(-16)}{-3-7}= \frac{y-12}{x-(-3)}](https://tex.z-dn.net/?f=%20%5Cfrac%7B12-%28-16%29%7D%7B-3-7%7D%3D%20%5Cfrac%7By-12%7D%7Bx-%28-3%29%7D%20%20)
![\frac{28}{-10}= \frac{y-12}{x+3}](https://tex.z-dn.net/?f=%5Cfrac%7B28%7D%7B-10%7D%3D%20%5Cfrac%7By-12%7D%7Bx%2B3%7D%20)
![28(x+3)=-10(y-12)](https://tex.z-dn.net/?f=28%28x%2B3%29%3D-10%28y-12%29)
![28x+84=-10y+120](https://tex.z-dn.net/?f=28x%2B84%3D-10y%2B120)
![28x+10y-36=0](https://tex.z-dn.net/?f=28x%2B10y-36%3D0)
, divide by 2 to simplify:
![14x+5y-18=0](https://tex.z-dn.net/?f=14x%2B5y-18%3D0)
similarly, the equation of Y is found using the points (0, -14) and (11, 8):
![\frac{-14-8}{0-11}= \frac{y-(-14)}{x-0}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-14-8%7D%7B0-11%7D%3D%20%5Cfrac%7By-%28-14%29%7D%7Bx-0%7D%20%20)
![\frac{-22}{-11}= \frac{y+14}{x}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-22%7D%7B-11%7D%3D%20%5Cfrac%7By%2B14%7D%7Bx%7D%20%20)
![2= \frac{y+14}{x}](https://tex.z-dn.net/?f=2%3D%20%5Cfrac%7By%2B14%7D%7Bx%7D%20%20)
![2x-y-14=0](https://tex.z-dn.net/?f=2x-y-14%3D0)
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: <span>(4, −6), because this point makes both the equations true</span>