all of the ordered pairs that are solutions to the following system of inequalities.
–5x+y<8
5x>4y–6
The steps to solve this system of inequalities are as follows:
1. Rearrange the inequalities to solve for y in terms of x:
-5x + y < 8
y < 5x + 8
5x > 4y - 6
5x > 4y - 6
5x + 6 > 4y
(5/4)x + 6/4 > y
y < (5/4)x + 3/2
2. Graph the two inequalities on the coordinate plane:
The first inequality, y < 5x + 8, is a dotted line with a slope of 5, passing through the point (0, 8).
The second inequality, y < (5/4)x + 3/2, is a dotted line with a slope of 5/4, passing through the point (0, 3/2).
3. Shade the region below both lines, as the solution to the system is the overlapping region.
4. The ordered pairs that are solutions to the system of inequalities are all the points within the shaded region on the coordinate plane.