Introduction to graphing systems of linear inequalities | Algebra II | Khan Academy

TL;DR

Graphing a system of inequalities to find the overlapping solution set.

Transcript

Graph the solution set for this system. It's a system of inequalities. We have y is greater than x minus 8, and y is less than 5 minus x. Let's graph the solution set for each of these inequalities, and then essentially where they overlap is the solution set for the system, the set of coordinates that satisfy both. So let me draw a coordinate axes ... Read More

Key Insights

• 📈 Graphing a system of inequalities involves graphing the boundary lines for each inequality.
• 😫 The solution set is found in the region where the shaded regions of each inequality overlap.
• 😥 Testing points can help determine if they are part of the solution set.
• 🫥 The type of line used (solid or dotted) depends on whether the inequality includes or excludes the line.

Questions & Answers

Q: How do you graph the boundary line for each inequality in a system of inequalities?

To graph the boundary line, identify the equation representing the inequality and plot points to determine the slope and y-intercept. Connect the plotted points with a line, making it solid or dotted based on whether the inequality includes or excludes the line.

Q: How do you determine which region represents the solution set?

The solution set is the region where the two inequalities overlap. Graph each inequality separately and observe where the shaded regions intersect.

Q: Why are the boundary lines sometimes solid and other times dotted?

The type of line used depends on whether the inequality includes or excludes the line. If the inequality includes the line, a solid line is used. If the inequality excludes the line, a dotted line is used.

Q: How can you test if a point is part of the solution set?

Substitute the x and y values of a point into both inequalities. If the values satisfy both inequalities, the point is part of the solution set. If not, the point is not part of the solution set.

Summary & Key Takeaways

• The video demonstrates how to graph a system of inequalities and find the solution set.

• It provides step-by-step instructions on graphing the boundary lines for each inequality.

• The solution set is found by identifying the region where the two inequalities overlap.