Graph the solution to the following system of inequalities. y > -2x+7, y ≤ 3x-8

The solution to the system of inequalities y > -2x+7, y ≤ 3x-8 is the set of points ( (x,y) pairs ) in the intersection of the regions these inequalities are true for, as shown in the graph by the intersection of the blue and red colors.

What are system of inequalities?

When mathematical expressions are compared, with non-strict equality, then such mathematical statements are called mathematical inequalties.

A collection of inequalities for which we consider common solution for all inequalities is called a system of inequalities.

How to draw regions covered by inequalities?

Suppose there is inequality given as: y ≥ f(x)

The region it covers is the region of value pairs (x,y) for which this inequality holds true.

We've to draw the region covered by it.

For a function y = f(x), there is y > f(x) on one side of the graph of the function y = f(x) in XY plane, and on other side there is y < f(x).

We just need to figure out this fact at 1 point on either side of the graph of the function y = f(x) , and then the area where y > f(x) is true, along with the curve of the function y = f(x) is included in the region covered by inequality y ≥ f(x)

For this case, the inequalities given are:

y > -2x+7, y ≤ 3x-8

Their solution is the points lying in the intersection of the regions these inequalities are true for, as shown in the graph by the intersection of the blue and red colors.