To find the intersection points of the system of equations, we first need to graph the equations on the same coordinate plane.
For the first equation 3x-2y=-4, we can rewrite it in slope-intercept form as y = (3/2)x + 2. This equation has a y-intercept of 2 and a slope of 3/2.
For the second equation x-5y=3, we can rewrite it in slope-intercept form as y = (1/5)x - 3/5. This equation has a y-intercept of -3/5 and a slope of 1/5.
When we graph both equations on the same coordinate plane, we will see that they intersect at the point (1, -1).
Therefore, the solution to both equations is x = 1 and y = -1.