Creating and Solving Systems of Equations/Inequalities

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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 set of all points that satisfy all inequalities in the system.

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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 dashed or solid line. Then, shade the region that satisfies the inequality (above for 'greater than', below for 'less than').

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What does it mean if a line is dashed in a graph of an inequality?

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A dashed line indicates that the points on the line are not included in the solution set (for inequalities like < or >).

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What does it mean if a line is solid in a graph of an inequality?

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A solid line indicates that the points on the line are included in the solution set (for inequalities like ≤ or ≥).

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

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To determine if a point is a solution, substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

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What is the purpose of using systems of equations in real-life problems?

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Systems of equations are used to find the values of variables that satisfy multiple conditions simultaneously, often representing constraints in real-life scenarios.

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What is the substitution method in solving systems of equations?

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The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

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What is the elimination method in solving systems of equations?

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The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the remaining variable.

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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 represents all possible solutions to a system of inequalities, where all constraints are satisfied.

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How do you find the intersection point of two lines?

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To find the intersection point, solve the system of equations formed by the two lines simultaneously, either by substitution or elimination.