Question

The two lines, X and Y, are graphed below:

Answer 1

Answer:c

Step-by-step explanation:

(4,-6), because this point makes both the equations true.

Answer 2

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:

$\frac{12-(-16)}{-3-7}= \frac{y-12}{x-(-3)}$

$\frac{28}{-10}= \frac{y-12}{x+3}$

$28(x+3)=-10(y-12)$

$28x+84=-10y+120$

$28x+10y-36=0$, divide by 2 to simplify:

$14x+5y-18=0$

similarly, the equation of Y is found using the points (0, -14) and (11, 8):

$\frac{-14-8}{0-11}= \frac{y-(-14)}{x-0}$

$\frac{-22}{-11}= \frac{y+14}{x}$

$2= \frac{y+14}{x}$

$2x-y-14=0$

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