The two lines, A and B, are graphed below: Line A is drawn by joining ordered pairs negative 3,18 and 9, negative 6. Line B is drawn by joining ordered pairs negative 5, negative 2 and 8,17 Determine the solution and the reasoning that justifies the solution to the systems of equations.A.)(−4, 6), because both the equations are true for this pointB.)(2, 8), because the graph of the two equations intersects at this pointC.)(2, 8), because neither of the two equations are true for this coordinate pointD.)(−4, 6), because the graph of the two equations intersects the x-axis at these points

we have that
line A points (-3,18)  and (9,-6)
line B points (-5,-2) and (8,17)

step 1
find the equation of the line A
find the slope m
m=[-6-18]/[9+3]-----> m=-24/12----> m=-2

with m=-2 and the point  (-3,18) find the equation of line A
y-y1=m*(x-x1)----> y-18=-2*(x+3)---> y=-2x-6+18
y=-2x+12

step 2
ind the equation of the line B
find the slope m
m=[17+2]/[8+5]-----> m=19/13

with m=19/13 and the point  (8,17) find the equation of line B
y-y1=m*(x-x1)----> y-17=(19/13)*(x-8)---> y=-(19/13)x-11.69+17
y=1.46x+5.31

step 3

determine the solution of the sistem
y=-2x+12
y=1.46x+5.31

we know that
the solution of the system of linear equations is the point of intersection of both graphs
using a graph tool
see the attached figure

the solution is the point (1.93, 8.13)-----> (2,8)

therefore

the answer is the option
B.)(2, 8), because the graph of the two equations intersects at this point