Systems of equations and inequalities

Front

What is a system of equations?

Back

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

Front

What does it mean for a system of equations to have a unique solution?

Back

It means there is exactly one set of values for the variables that satisfies all equations in the system.

Front

What is an intersection point in the context of systems of equations?

Back

The point where the graphs of the equations meet, representing the solution to the system.

Front

What is a system of inequalities?

Back

A set of two or more inequalities with the same variables.

Front

What does it mean for a system of inequalities to be consistent?

Back

It means there is at least one solution that satisfies all inequalities.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

How do 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 the feasible region in a system of inequalities?

Back

The area on a graph where all the inequalities overlap, representing all possible solutions.

Front

What does shading represent in the graph of inequalities?

Back

Shading indicates the region where the solutions to the inequality are located.

Front

What is the difference between 'no solution' and 'infinitely many solutions' in a system of equations?

Back

'No solution' means the lines are parallel and never intersect; 'infinitely many solutions' means the lines coincide.