Systems & Inequalties review

Front

What is a solid line in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set, representing 'greater than or equal to' (≥) or 'less than or equal to' (≤).

Front

What does the inequality 5 ≥ x represent?

Back

It represents all values of x that are less than or equal to 5.

Front

How do you solve a system of inequalities by graphing?

Back

1. Graph each inequality on the same coordinate plane. 2. Identify the overlapping region that satisfies all inequalities.

Front

What is the solution to the system of equations 5x - 4y = -16 and x + 2y = -6?

Back

The solution is (-4, -1).

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means that the equations represent the same line, and there are countless points that satisfy both equations.

Front

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

Back

A solid line includes the boundary points (≥ or ≤), while a dashed line does not include the boundary points (> or <).

Front

How do you determine the number of solutions in a system of equations?

Back

By analyzing the graphs: if lines intersect at one point, there is one solution; if they are parallel, there is no solution; if they overlap, there are infinitely many solutions.

Front

What does the inequality x > 2 mean in a graph?

Back

It represents all values of x that are greater than 2, shown as a dashed line starting from 2 and extending to the right.

Front

What is the graphical representation of y < -4?

Back

It is a horizontal dashed line at y = -4, with the area below the line shaded.

Front

What does the term 'system of inequalities' refer to?

Back

A set of two or more inequalities with the same variables that are solved together.