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 system of equations to have no solution?

Back

It means the equations represent parallel lines that never intersect.

Front

What is the graphical representation of a system of equations with infinitely many solutions?

Back

The equations represent the same line, meaning they overlap completely.

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 inequalities, it is a solution.

Front

What is the difference between a solution to an equation and a solution to an inequality?

Back

A solution to an equation is a specific point, while a solution to an inequality is a range of values.

Front

What does the term 'feasible region' refer to in the context of inequalities?

Back

The area on a graph where all the solutions to a system of inequalities exist.

Front

How can you graph a system of inequalities?

Back

Graph each inequality as a line, then shade the appropriate region that satisfies all inequalities.

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

What does it mean for two lines to be skew?

Back

Skew lines are lines that do not intersect and are not parallel, typically found in three-dimensional space.