Systems of Equations & Inequalities Review

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What is a system of equations?

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A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect on a graph.

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What does it mean to solve a system of equations?

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To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

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What is substitution in solving systems of equations?

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Substitution is a method where one equation is solved for one variable, and that expression is substituted into the other equation.

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What is the difference between a solid line and a dotted line when graphing inequalities?

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A solid line indicates that the points on the line are included in the solution (≥ or ≤), while a dotted line indicates that the points on the line are not included (> or <).

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

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A point is a solution if it satisfies all inequalities in the system when substituted into them.

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

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The solution is represented by the point(s) where the graphs of the equations intersect.

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What does the term 'feasible region' refer to in the context of inequalities?

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The feasible region is the area on a graph that satisfies all inequalities in a system, representing all possible solutions.

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

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It means that the lines representing the equations are parallel and never intersect.