Systems 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 is the difference between systems of equations and systems of inequalities?

Back

Systems of equations have 1 solution, no solution, or infinite solutions while systems of inequalities can have a range of solutions.

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.

Front

How do you graph a system of inequalities?

Back

To graph a system of inequalities, graph each inequality on the same coordinate plane, using dashed lines for < or > and solid lines for ≤ or ≥. The solution is the overlapping shaded region.

Front

What is the slope-intercept form of a linear inequality?

Back

The slope-intercept form of a linear inequality is written as y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the shaded region represent in a graph of inequalities?

Back

The shaded region represents all the possible solutions to the inequality.

Front

What is the significance of the boundary line in a system of inequalities?

Back

The boundary line separates the coordinate plane into two regions: one that satisfies the inequality and one that does not.

Front

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

Back

Substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What does it mean if a system of inequalities has no solution?

Back

A system of inequalities has no solution if the shaded regions do not overlap, meaning there are no points that satisfy all inequalities.

Front

What is the graphical representation of the inequality y > 2x - 4?

Back

The graph of y > 2x - 4 is a dashed line for y = 2x - 4 with the area above the line shaded.