Solving Systems of Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤) instead of an equal sign.

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.

Front

What does it mean if a point is a solution to a linear inequality?

Back

A point is a solution to a linear inequality if, when substituted into the inequality, it makes the inequality true.

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

How can you determine if a point is a solution to the inequality y > -x + 1?

Back

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

Front

What is the solution set of a system of linear inequalities?

Back

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

Front

What does the inequality y < x + 2 represent graphically?

Back

It represents all the points below the line y = x + 2, not including the line itself.

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 point (0,0) in relation to the inequality y > -x + 1?

Back

The point (0,0) is not a solution to the inequality y > -x + 1 because substituting (0,0) does not satisfy the inequality.

Front

What is a feasible region in the context of linear inequalities?

Back

A feasible region is the area on a graph that satisfies all the constraints of a system of linear inequalities.