Graph the solution set of each system of inequalities. { -2 x+y ≤ 8 -x+y ≥ 2 .

Graph the solution set of each system of inequalities. { ...

Key Concepts

Graphing Linear Inequalities

This concept involves plotting a linear equation and then shading the region of the graph that satisfies the inequality. The inequality determines which side of the boundary line (drawn as a solid line for ? or ?, and dashed for < or >) is included in the solution. It is essential for visually representing the solution set of an inequality on the Cartesian plane.

Systems of Linear Inequalities

A system of linear inequalities is a set of two or more inequalities that are considered simultaneously. The solution to the system is the intersection of the solution sets of each individual inequality, meaning it is the region that satisfies all inequalities at the same time. This concept is particularly useful in optimization and decision-making problems.

Feasible Region

The feasible region is the common area where all the inequalities in a system overlap. It represents all the possible solutions that satisfy every inequality in the system. Understanding the feasible region is crucial for problems in linear programming and systems analysis, as it defines the set of potential solutions.

Transcript

00:01 Here in this problem we have to graph the solution set of the given set of inequality which is minus 2x plus y is less than or equals to 8 and minus x plus y is greater than or equals to 2 now first of all we'll graph this inequality and to do so i'll be graphing the equation minus 2x plus y is equals to 8 and now i'll be making a table by using the table we can graph this equation easily now we'll be taking different value of x so that we can find out different values of y you can take any value it's up to you i'm taking x as minus 6 so i'm getting y as minus 4 after putting the value of x as minus 6 here we'll get y as minus 4 now if i take x as minus 4 i get y as 0 so we have obtained two points and by using these two points i'll make a graph so i'll take a graph paper now so i'll be marking these two points on a graph paper first point is minus six comma minus four so minus six x here is minus six and minus four this point is minus four so we obtained this point and the next is minus four comma zero so x is minus 4 and y is 0.

01:39 So this point will represent minus 4 comma 0.

01:43 Now i'll be joining these two point to make a line.

01:48 So i'll get so obtained this line now the solution set of this inequality that is minus 2x plus y is less than equals to it will lie on either this region or this region.

02:11 It depends.

02:13 So we have to check and to do so i i'll be taking a point on either side of the line, this side or this side.

02:20 So i'm taking this point because it's very convenient point to take 0 .0.

02:26 Here, x coordinate is 0 and y coordinate is also 0...

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