Chapter 6 Review - Systems of Equations and Inequalities

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

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols like <, >, ≤, or ≥.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation. 2. Use a dashed line for < or >, and a solid line for ≤ or ≥. 3. Shade the region that satisfies the inequality.

Front

What is the difference between a consistent and inconsistent system of equations?

Back

A consistent system has at least one solution, while an inconsistent system has no solutions.

Front

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

Back

It means that the equations represent the same line, and every point on that line is a solution.

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. If it satisfies all equations, it is a solution.

Front

What is the substitution method for solving systems of equations?

Back

The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method for solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What does the graph of a system of inequalities look like?

Back

It shows the feasible region where all inequalities overlap, often shaded to indicate possible solutions.