Solving Systems of Linear Inequalities(with 2 variables)

Front

What is a system of linear inequalities?

Back

A system of linear inequalities is a set of two or more inequalities with the same variables. The solution is the region where the graphs of the inequalities overlap.

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, depending on whether the inequality is strict (<, >) or inclusive (≤, ≥). Then shade the region that satisfies the inequality.

Front

What does the inequality y > x + 1 represent on a graph?

Back

It represents the region above the line y = x + 1, not including the line itself.

Front

What does the inequality y ≤ -x + 1 represent on a graph?

Back

It represents the region below the line y = -x + 1, including the line itself.

Front

What is the solution to the system of inequalities?

Back

The solution to a system of inequalities is the set of all points that satisfy all inequalities in the system, typically represented as a shaded region on a graph.

Front

How can you determine if a point is a solution to a system of inequalities?

Back

To determine if a point is a solution, substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What does the graph of x < -1 look like?

Back

The graph of x < -1 is a vertical dashed line at x = -1, with shading to the left, indicating all values less than -1.

Front

How do you rewrite the inequality 3x - 6y > 12 in y= form?

Back

To rewrite it, isolate y: 6y < 3x - 12, so y < (1/2)x - 2.

Front

What is the significance of a dashed line in graphing inequalities?

Back

A dashed line indicates that points on the line are not included in the solution set for strict inequalities (< or >).

Front

What does the ordered pair (0,0) represent in the context of a system of inequalities?

Back

The ordered pair (0,0) represents a point that may or may not be a solution to the system, depending on whether it satisfies all inequalities.