Graphing Systems

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

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

Tags

CCSS.HSA.REI.D.12

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

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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.

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

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

Tags

CCSS.8.EE.C.8A

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

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

Tags

CCSS.HSA.REI.D.12

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

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

Tags

CCSS.8.EE.C.8A

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How can you graph a system of inequalities?

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

Tags

CCSS.HSA.REI.D.12

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

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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.

Tags

CCSS.8.EE.C.8B

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

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

Tags

CCSS.8.EE.C.8A

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

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

Tags

CCSS.HSA.REI.D.12

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

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