Graphing Systems

Front

What are the vertices of a feasible region in a graphing system?

Back

The vertices of a feasible region are the corner points of the shaded area that represents all possible solutions to a system of inequalities.

Front

How do you determine if a point is a solution to a system of equations?

Back

To determine if a point is a solution, substitute the x and y values of the point into each equation. If the point satisfies all equations, it is a solution.

Front

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

Back

A system of equations has one solution when the graphs of the equations intersect at exactly one point.

Front

What is a feasible region in the context of graphing systems?

Back

A feasible region is the area on a graph that satisfies all constraints of a system of inequalities.

Front

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

Back

The intersection point represents the solution to the system, where all equations are satisfied simultaneously.

Front

How can you graph a system of inequalities?

Back

To graph a system of inequalities, first graph the boundary lines as equations, then shade the appropriate regions that satisfy the inequalities.

Front

What is the difference between a solution and a feasible solution in a graphing system?

Back

A solution is a point that satisfies all equations, while a feasible solution is a point that satisfies all constraints in a system of inequalities.

Front

What does it mean if a system of equations has no solution?

Back

A system has no solution if the graphs of the equations are parallel and never intersect.

Front

How do you find the coordinates of the vertices of a feasible region?

Back

The coordinates of the vertices can be found by solving the equations of the boundary lines at their points of intersection.

Front

What is the role of the objective function in linear programming?

Back

The objective function is the equation that needs to be maximized or minimized within the feasible region.