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 graph a system of inequalities?

Back

To graph a system of inequalities, first graph each inequality as if it were an equation. Then, shade the appropriate region (above or below the line) based on the inequality sign. The solution is where the shaded regions overlap.

Front

What does the inequality y ≥ mx + b represent?

Back

This inequality represents all points on or above the line y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean to shade above the line in a graph?

Back

Shading above the line indicates that the solutions to the inequality include all points where the y-value is greater than the y-value of the line.

Front

What does it mean to shade below the line in a graph?

Back

Shading below the line indicates that the solutions to the inequality include all points where the y-value is less than the y-value of the line.

Front

What is the solution set of the inequality y < -x + 2?

Back

The solution set includes all points below the line y = -x + 2.

Front

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

Back

To determine if a point is a solution, substitute the x and y values of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the significance of the boundary line in an inequality?

Back

The boundary line represents the points where the inequality changes from true to false. For '≤' or '≥', the line is included in the solution; for '<' or '>', it is not.

Front

What does the inequality y > -x - 1 represent graphically?

Back

Graphically, it represents all points above the line y = -x - 1, not including the line itself.

Front

What is the difference between 'y <' and 'y ≤'?

Back

'y <' means the line is not included in the solution set, while 'y ≤' means the line is included.