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

Key Concepts

System of Inequalities

A system of inequalities consists of multiple inequalities that are considered simultaneously. The solution to the system is the set of all points that satisfy every inequality in the system, and graphing this system often involves finding the intersection of the individual solution sets.

Graphing Inequalities on the Coordinate Plane

Graphing inequalities involves representing the solutions on a coordinate plane. This includes drawing the boundary lines of the inequalities and shading the regions that satisfy each inequality. The final solution set is given by the overlap of all shaded regions.

Boundary Lines and Inequality Symbols

Inequalities can have 'less than or equal to' (?) or 'greater than or equal to' (?) symbols, which indicate that the boundary line is included in the solution set. In contrast, symbols like '<' or '>' indicate that the boundary line is not included. Distinguishing between these affects how the boundaries are drawn, using solid lines for inclusive and dashed lines for exclusive boundaries.

Intersection of Solution Sets

To solve a system of inequalities, one must find the common area that satisfies all inequalities simultaneously. This involves overlaying the graph of each inequality and determining the region where they all overlap on the coordinate plane.

Transcript

00:01 Here in this problem we have to graph the solution set for the given set of inequalities which is x is less than or equals to five and the next one is x is greater than or equals to two and y is greater than one so first of all i'll be finding or you could say graphing the solution set for the first inequality and to do so i'll be graphing the equation x equals to five so let's take a graph paper now so this is a graph paper now we have to graph x equals to 5 so x equal 5 will be this line this line will represent x equals to 5 now the solution set for the first inequality would be either on this side or this side it totally depends so we'll go to check with whether this side is our solution set or this side for that i have to take any one point you can take on either side this side or this side or this side but i'm taking it on origin which is 0 comma 0 so i'll be plugging these values in the inequality here x coordinate is 0 so we get 0 is less than or equals to 5 which is true 0 is less than 5 the inequality is true here so the solutions that would lie on this side towards the origin now same thing will do for x is greater than or equals to 2 for that i'll be drafting the equation x equal to 2 so x equal to 2 will be this line so this line will represent x equals to 2 now again we have to check that whether this side is our solution or this side for that again i'm taking a point on origin so x is 0 here so i'll plotting the value of x as 0 so 0 is greater than or equals to 2 but this is wrong this time zero is cannot be greater than 2 so the solution set would lie on this side away from the origin not towards the origin because here the inequality fails so this side would be a region of solution now the last one is why is greater than one now for this we have to graph the equation y equals to one so y equals to one will be this line here this line will represents y equals to one now again we have to check whether but there is one problem here here y is greater than one it is there is no equal sign here so we cannot make a solid line we have to make a dotted line because equal sign is not there so let's rub this equation is line and we should make a dotted line here the reason behind it i've told you that why is greater than one it is written it is there is no equal sign is there that is why we have to make a dotted line now again we have to check at whether this side is our solution or this side.

03:25 So again i'm taking a point on origin and plugging these value here.

03:29 So why coordinate is zero? so zero is greater than one which is wrong.

03:34 Zero cannot be greater than one...

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