Systems of equations and inequalities

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

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 region where the inequalities overlap on a graph.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line. Use a dashed line for < or > and a solid line for ≤ or ≥. Then shade the appropriate region based on the inequality.

Front

What does it mean to solve a system of inequalities by graphing?

Back

Solving a system of inequalities by graphing involves plotting each inequality on the same coordinate plane and identifying the region where the solutions overlap.

Front

What is the significance of the shaded region in a graph of inequalities?

Back

The shaded region represents all the possible solutions that satisfy the inequality.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the boundary line, while non-strict inequalities (≤, ≥) include the boundary line.

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 is the graphical representation of the solution (6, 3) in a system of inequalities?

Back

The point (6, 3) is a specific coordinate on the graph that represents a solution to the system of inequalities.

Front

What does the notation y > -x - 1 represent?

Back

This notation represents a linear inequality where the region above the line y = -x - 1 is shaded, indicating all points where y is greater than -x - 1.

Front

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

Back

The boundary line separates the graph into two regions, one where the inequality holds true and one where it does not.