Systems of Equations and 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 set of values that satisfy all equations simultaneously.

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What is the elimination method for 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.

Front

What is the substitution method for 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.

Front

What does it mean for a solution to satisfy a system of inequalities?

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A solution satisfies a system of inequalities if it makes all inequalities true when substituted into them.

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How do you graph a linear inequality?

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To graph a linear inequality, first graph the corresponding equation as a line, then shade the region that satisfies the inequality.

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What is the difference between a strict inequality and a non-strict inequality?

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A strict inequality (e.g., < or >) does not include the boundary line, while a non-strict inequality (e.g., ≤ or ≥) includes the boundary line.

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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 the values of the variables satisfy all equations.

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What is a feasible region in the context of inequalities?

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A feasible region is the area on a graph where all constraints (inequalities) are satisfied, representing all possible solutions.

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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 and check if all inequalities hold true.

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What is the role of coefficients in a system of equations?

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Coefficients determine the slope and position of the lines represented by the equations, affecting the solution set.