Solving Systems of Inequalities by Graphing 03:51 minutes

Video Transcript

Transcript Solving Systems of Inequalities by Graphing

Frank, the insurance man, is on a flight to Peru to track down Adventure Mike in the Peruvian jungle. Adventure Mike needs to renew his Ultra Danger Insurance Package. Otherwise, he will not have any insurance on his various adventures.

The system of linear inequalities

Frank takes out his phone to look at the text message that he received a few days ago from Adventure Mike. The text message provides a hint as to which region in the jungle Adventure Mike is searching for ancient relics. Frank knows that Adventure Mike likes to communicate in riddles. He recognizes Mike's missive as a system of linear inequalities.

Good thing Frank knows how to solve a system of linear inequalities by graphing. Let's see how Frank solves the system of linear inequalities. Here's a map of the surrounding region. Since we have a system of linear inequalities, we need to include the x- and y-axes in order to graph them. Our starting point, or the origin, is the city of Cuzco.

We need to graph the system of inequalities. Each inequality is written in slope-intercept form. For the first inequality, 1 is the y-intercept or the ordered pair (0, 1). To find the second point, we use the slope of the line. The slope of the line is -2 or -2 over 1. We move down 2 from the y-intercept and right 1. The resulting ordered pair is (1, -1).

Less than or Equal to

Since the inequality represents 'Less than or Equal to', the graph of the inequality is a solid line. All of the points to the left of the inequality are true. We can shade to the left of the inequality line. For the second inequality, 2 is the y-intercept, or the ordered pair (0, -2). To find the second point, we use the slope of the line.

Less than

The slope of the line is 3 over 2. We move up 3 from the y-intercept and right 2. The resulting ordered pair is (2, 1). Since the inequality represents 'Less than', the graph of the inequality is a dotted line. Since all of the points to the right of the inequality are true. We can shade to the right of the inequality line.

The solution to the system of inequalities is where the shading from each inequality overlaps. Frank knows in which part of the jungle to look, so he sets off to find Adventure Mike. Wow! Frank finds an ancient Incan temple. But, what is carved into the side of it? Adventure Mike has left another hint!

Frank pulls out his map again so he can crack this clue and narrow down the possible whereabouts of Adventure Mike. We need to graph the inequality. The inequality is written in slope-intercept form. For the first inequality, -4 is the y-intercept or the ordered pair (0, -4). To find the second point, we use the slope of the line. The slope of the line is 1 over 4. We move up 1 from the y-intercept and right 4. The resulting ordered pair is (4, -3).

Greater than or Equal to

Since the inequality represents 'Greater than or Equal to', the graph of the inequality is a solid line. All of the points above the inequality are true. We can shade above the inequality line. The solution to the system of inequalities is where the shading from each inequality overlaps. Now Frank knows exactly where to go...Oh, so THAT'S why Adventure Mike sent those strange messages in the first place.