Unit 7 Review - Systems

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What is a system of inequalities?

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A system of inequalities is a set of two or more inequalities with the same variables. The solution is the region where the graphs of the inequalities overlap.

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How do you graph a linear inequality?

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To graph a linear inequality, first graph the corresponding linear equation as a solid line (for ≤ or ≥) or a dashed line (for < or >). Then shade the region that satisfies the inequality.

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What does the solution to a system of equations represent?

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The solution to a system of equations represents the point(s) where the graphs of the equations intersect, indicating the values of the variables that satisfy all equations in the system.

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What is substitution in solving systems of equations?

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Substitution is a method where you solve one equation for one variable and then substitute that expression into the other equation to find the values of the variables.

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What is the graphical method for solving systems of equations?

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The graphical method involves plotting each equation on the same graph and identifying the point(s) where the lines intersect, which represent the solution(s) to the system.

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What is a feasible region in the context of linear programming?

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The feasible region is the area on a graph that satisfies all constraints of a linear programming problem, typically represented by the intersection of the graphs of the inequalities.

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What is the difference between consistent and inconsistent systems?

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A consistent system has at least one solution (intersecting lines), while an inconsistent system has no solutions (parallel lines that never intersect).

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What does it mean for a system of equations to be dependent?

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A dependent system has infinitely many solutions, meaning the equations represent the same line when graphed.

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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 coordinates of the point into each equation. If the point satisfies all equations, it is a solution.

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What is the standard form of a linear equation?

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