Question 24981
the coordinates at the point of intersection must solve both equations 
because the point is ON both equations, so just make sure that is true
(1) y = 3/4x - 4
(2) y = (-1/2)x + 6
subtract  (2) from (1) 
(3) 0 = (3/4x - 4) - ((-1/2)x + 6)
(4) 0 = (5/4)x - 10
(5) (5/4)x = 10
(6) 5x = 40
(7) x = 8
now solve for y in either equation
(8) y = ((3/4)*8) - 4
(9) y = 6 - 4
(10) y = 2
that means the point (8, 2) is on both lines , thus it is the intersection
check it with the other equation
(11) 2 = ((-1/2) * 8) + 6
is this true? 
(12) 2 = -4 + 6
yes
just go through this whith the other equations and you'll get the intersections
remember that TWO lines have to intersect unless they're parallel (same slope)
THREE lines do not necessarily have to intersect all at the same point, though
taken in pairs, they will have intersections, though