Question

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

Line X is drawn by joining ordered pairs negative 3,12 and 7,negative 16. Line Y is drawn by joining ordered pairs 0, negative 14 and 11, 8

Determine the solution and the reasoning that justifies the solution to the systems of equations.

 (2, 7), because this point is true for both the equations



(4, −6), because this point lies only on one of the two lines

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

(2, 7), because the lines intersect the x-axis at these points

Answer 1

Answer:c

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:


`(12-(-16))/(-3-7)= (y-12)/(x-(-3))`


`(28)/(-10)= (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):


`(-14-8)/(0-11)= (y-(-14))/(x-0)`


`(-22)/(-11)= (y+14)/(x)`


`2= (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