Systems of Equations and Inequalities Review

Front

What is a system of equations?

Back

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

Front

What does it mean for a system of equations to have one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

What does it mean for a system of equations to have no solutions?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

The lines representing the equations coincide, meaning they are the same line.

Front

How do you represent a linear inequality?

Back

Using symbols like <, >, ≤, or ≥ to show the relationship between two expressions.

Front

What is the graphical representation of y ≤ mx + b?

Back

A shaded region below the line y = mx + b, including the line itself.

Front

What is the graphical representation of y > mx + b?

Back

A shaded region above the line y = mx + b, excluding the line itself.

Front

How do you find the solution to a system of inequalities?

Back

By graphing each inequality and identifying the overlapping shaded region.

Front

What is the significance of the x and y intercepts in a linear equation?

Back

They are the points where the line crosses the x-axis and y-axis, respectively.

Front

How do you convert a word problem into a system of inequalities?

Back

Identify the variables, constraints, and relationships described in the problem.