LT.6: Students find solution to a system of inequalities

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Front

What does it mean for a point to be a solution to a system of inequalities?

Back

A point is a solution to a system of inequalities if it satisfies all the inequalities in the system, meaning it lies in the overlapping region of the graphs of the inequalities.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line, then shade the region that satisfies the inequality (above or below the line).

Front

What is the difference between a dashed line and a solid line in graphing inequalities?

Back

A dashed line indicates that points on the line are not included in the solution (for < or >), while a solid line indicates that points on the line are included (for ≤ or ≥).

Front

What does the inequality y ≤ 3x represent graphically?

Back

It represents all points on or below the line y = 3x.

Front

How can you determine if a point is a solution to an inequality?

Back

Substitute the coordinates of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the solution set of a system of inequalities?

Back

The solution set is the region on the graph where the shaded areas of all inequalities overlap.

Front

What does the inequality y > -2x + 4 represent?

Back

It represents all points above the line y = -2x + 4.

Front

How do you solve a system of inequalities by graphing?

Back

Graph each inequality on the same coordinate plane, shade the appropriate regions, and identify the overlapping shaded area as the solution.

Front

What is the significance of the intersection of two inequalities?

Back

The intersection represents the set of points that satisfy both inequalities simultaneously.