Learning Outcome
- Identify whether an ordered pair is in the solution set of a linear inequality
The graph below shows the region of values that makes the inequality 3x+2y≤63x+2y≤6 true (shaded red), the boundary line 3x+2y=63x+2y=6, as well as a handful of ordered pairs. The boundary line is solid because points on the boundary line 3x+2y=63x+2y=6 will make the inequality 3x+2y≤63x+2y≤6 true.
You can substitute the x and y-values of each of the (x,y)(x,y) ordered pairs into the inequality to find solutions. Sometimes making a table of values makes sense for more complicated inequalities.
Ordered Pair | Makes the inequality 3x+2y≤63x+2y≤6 a true statement | Makes the inequality 3x+2y≤63x+2y≤6 a false statement |
---|---|---|
(−5,5)(−5,5) | 3(−5)+2(5)≤6−15+10≤6−5≤63(−5)+2(5)≤6−15+10≤6−5≤6 | |
(−2,−2)(−2,−2) | 3(−2)+2(–2)≤6−6+(−4)≤6–10≤63(−2)+2(–2)≤6−6+(−4)≤6–10≤6 | |
(2,3)(2,3) | 3(2)+2(3)≤66+6≤612≤6 | |
(2,0) | 3(2)+2(0)≤66+0≤66≤6 | |
(4,−1) | 3(4)+2(−1)≤612+(−2)≤610≤6 |
If substituting (x,y) into the inequality yields a true statement, then the ordered pair is a solution to the inequality, and the point will be plotted within the shaded region or the point will be part of a solid boundary line. A false statement means that the ordered pair is not a solution, and the point will graph outside the shaded region, or the point will be part of a dotted boundary line.
Example
Use the graph to determine which ordered pairs plotted below are solutions of the inequality x–y<3.
The following video shows an example of determining whether an ordered pair is a solution to an inequality.
Example
Is (2,−3) a solution of the inequality y<−3x+1?
The following video shows another example of determining whether an ordered pair is a solution to an inequality.
Candela Citations
- Use a Graph Determine Ordered Pair Solutions of a Linear Inequalty in Two Variable. Authored by: James Sousa (Mathispower4u.com) . Located at: https://youtu.be/GQVdDRVq5_o. License: CC BY: Attribution
- Ex: Determine if Ordered Pairs Satisfy a Linear Inequality. Authored by: James Sousa (Mathispower4u.com) . Located at: https://youtu.be/-x-zt_yM0RM. License: CC BY: Attribution
- Unit 13: Graphing, from Developmental Math: An Open Program. Provided by: Monterey Institute of Technology. Located at: http://nrocnetwork.org/dm-opentext. License: CC BY: Attribution