Graph the system of inequalities y< 5x-1, y\geq-3x+4

which two quadrants does the solution lie in?

The inequalities that are given in this item are given below,
       y < 5x - 1
       y ≥ -3x +4

We dropped the inequalities sign to solve for the values of x and y for the intersection.
      y = 5x - 1
      y = 3x + 4

Substituting the y from the first equation to the y of the second equation,
     5x - 1 = 3x + 4
    2x = 5
    x = 5/2

Substituting for y,
      y = (5)(5/2) - 1
      y = 25/2 - 1 = 11.5

The intersection is (5/2, 11.5)

The solutions of the system of inequalities lie in the 3rd and 4th quadrants.