Creating and Solving Systems of Equations/Inequalities

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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.

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How do you represent a word problem as a system of equations?

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Identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the problem's constraints.

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What does it mean to solve a system of equations?

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To find the values of the variables that satisfy all equations in the system simultaneously.

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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 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 an inequality?

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An inequality is a mathematical statement that compares two expressions, showing that one is less than, greater than, less than or equal to, or greater than or equal to the other.

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How do you graph a system of inequalities?

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Graph each inequality on the same coordinate plane, shading the region that satisfies each inequality. The solution is where the shaded regions overlap.

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What is a feasible region in the context of inequalities?

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The feasible region is the area on a graph where all constraints of a system of inequalities are satisfied.

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What does it mean for a solution to be 'bounded' in a system of inequalities?

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A bounded solution means that the feasible region is enclosed, and there are limits to the values of the variables.

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What does it mean for a solution to be 'unbounded' in a system of inequalities?

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An unbounded solution means that the feasible region extends infinitely in at least one direction.