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 point to be a solution to a system of equations?

Back

A point is a solution if it satisfies all equations in the system.

Front

How can you determine if a point is a solution to a system of equations?

Back

Substitute the point's coordinates into each equation and check if they hold true.

Front

What is the graphical representation of a system of equations?

Back

The intersection point(s) of the lines representing the equations.

Front

What are the possible outcomes when solving a system of equations?

Back

1. One solution (intersecting lines), 2. No solution (parallel lines), 3. Infinitely many solutions (same line).

Front

What is an inequality?

Back

A mathematical statement that compares two expressions using <, >, ≤, or ≥.

Front

How do you graph a linear inequality?

Back

Graph the corresponding equation as a line, then shade the appropriate region based on the inequality.

Front

What is the substitution method for solving systems of equations?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

What is the elimination method for solving systems of equations?

Back

Add or subtract equations to eliminate one variable, making it easier to solve for the other.

Front

What does it mean for two lines to be parallel in the context of systems of equations?

Back

They have the same slope but different y-intercepts, meaning they never intersect.