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

How do you determine if a point is part of the solution set for a system of inequalities?

Back

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

Front

What does the graph of an inequality represent?

Back

The graph of an inequality represents all the solutions to that inequality. It shows the region of the coordinate plane where the inequality holds true.

Front

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

Back

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

Front

How do you graph the inequality y > 2x - 4?

Back

1. Graph the line y = 2x - 4 using a dashed line. 2. Shade the region above the line, as it represents all points where y is greater than 2x - 4.

Front

What is the solution to the system of inequalities y < 2/3x - 3?

Back

The solution is the region below the line y = 2/3x - 3, which includes all points (x, y) that satisfy the inequality.

Front

How do you write an inequality from a graph?

Back

To write an inequality from a graph, identify the slope and y-intercept of the line, determine if the line is solid or dashed, and decide if the region is above or below the line.

Front

What does the notation y ≥ -2x + 3 indicate?

Back

The notation y ≥ -2x + 3 indicates that y is greater than or equal to the value of -2x + 3, including the points on the line.

Front

What is the significance of the intersection of two inequalities?

Back

The intersection of two inequalities represents the set of points that satisfy both inequalities simultaneously, forming the solution region.

Front

How can you check if a point (5, 1) is a solution to the system y < 2x - 4 and y > -2x + 3?

Back

Substitute (5, 1) into both inequalities: 1 < 2(5) - 4 and 1 > -2(5) + 3. If both are true, then (5, 1) is a solution.