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 if a system of equations has no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

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

Back

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

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 a system of inequalities?

Back

A set of two or more inequalities that are solved together, often represented graphically.

Front

What does it mean to shade a region in a graph of inequalities?

Back

Shading indicates the set of all possible solutions that satisfy the inequalities.

Front

What is the graphical representation of a solution to a system of equations?

Back

The point(s) where the graphs of the equations intersect.

Front

What is the difference between a solution and a feasible region in a system of inequalities?

Back

A solution is a specific point that satisfies all inequalities, while the feasible region is the area that contains all possible solutions.

Front

How can you tell if a point is in the feasible region of a system of inequalities?

Back

By substituting the point into the inequalities; if all inequalities are satisfied, the point is in the feasible region.

Front

What is the significance of the boundary line in a system of inequalities?

Back

The boundary line represents the points where the inequality changes from true to false.