Systems of Equations/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 the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution set, while a dashed line indicates they are not.

Front

What does the symbol '≥' indicate in an inequality?

Back

It indicates that the value is greater than or equal to.

Front

How do you determine the feasible region in a system of inequalities?

Back

By graphing each inequality and identifying the overlapping area 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 if a system of equations has no solution?

Back

It means the lines representing the equations are parallel and never intersect.

Front

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

Back

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