the coordinate grid shows the graph of four equations:
a coordinate grid is shown from negative 12 to positive 12 on the x axis and also on the y axis. line a passes through the ordered pairs negative 3, 4 and 9, negative 2. line b passes through the ordered pairs 2, 8 and 8, negative 8. line c passes through the ordered pairs negative 3, negative 4 and 4, 6. line d passes through the points 2, negative 2 and 5 and 6.
which set of equations has (5, 0) as its solution?
a and b
c and d
b and d
a and d

When you graph the following lines, the set of equations that has (5, 0) as its solution are lines A and B. You can see that both lines passes though the coordinate (5,0). Another way of determining if the given coordinate is a solution to the equation to to establish an equation using these points. In here, i will use the point - slope form.
for line A, we have (-3,4) and (9, -2)
y - y1 = m(x - x1)
y - 4 = (-2 - 4/9 -(-3))(x - (-3))
y - 4 = -(1/2)(x+3)
2y - 8 = -x - 3
2y = -x + 5

substitute (5,0)
2(0) = -5 + 5
0 = 0