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

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:









, divide by 2 to simplify:



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









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. 

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