REVIEW Systems of Linear Equations & Inequalities12.12.24

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Front

What does it mean for a system of equations to have infinitely many solutions?

Back

It means that there are an infinite number of points that satisfy all equations in the system.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

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 all equations are satisfied, it is a solution.

Front

What is an inequality?

Back

A mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other.

Front

What does it mean for a point to be part of the solution set of an inequality?

Back

It means that the point satisfies the inequality when its coordinates are substituted into it.

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 that makes the equation true, while a solution to an inequality is a range of values that satisfy the inequality.

Front

What is the significance of the intersection point of two lines in a system of equations?

Back

It represents the solution to the system, where both equations are satisfied.

Front

What does it mean if two lines are parallel in a system of equations?

Back

It means that the system has no solutions, as the lines never intersect.

Front

What is a feasible region in the context of inequalities?

Back

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