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 of a system of equations?

Back

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

Front

What is an inequality?

Back

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

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

What does shading a region in a graph of inequalities represent?

Back

It represents all the solutions that satisfy the inequality.

Front

How do you determine if a point is a solution to a system of inequalities?

Back

Substitute the point into each inequality; if it satisfies all, it is a solution.

Front

What is the difference between consistent and inconsistent systems of equations?

Back

Consistent systems have at least one solution; inconsistent systems have no solutions.

Front

What are infinite solutions in a system of equations?

Back

When the equations represent the same line, every point on the line is a solution.

Front

How do you solve a system of equations graphically?

Back

By plotting the equations on a graph and identifying the intersection point.

Front

What is the substitution method for solving systems of equations?

Back

Solving one equation for a variable and substituting that expression into the other equation.