Question

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

Which two quadrants does the solution lie in?

Answer 1

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.