Solving Systems of Equations & Inequalities Test

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What is a system of equations?

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A set of two or more equations with the same variables that are solved together.

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What is a solution to a system of equations?

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An ordered pair (x, y) that satisfies all equations in the system.

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What does it mean for a system of equations to have no solution?

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It means that the equations represent parallel lines that never intersect.

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What does it mean for a system of equations to have infinite solutions?

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It means that the equations represent the same line, so every point on the line is a solution.

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How do you graph a system of inequalities?

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Graph each inequality on the same coordinate plane and identify the feasible region where the shaded areas overlap.

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What is the feasible region in a system of inequalities?

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The area on the graph where all the inequalities are satisfied.

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What is the objective function in linear programming?

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A function that needs to be maximized or minimized, typically represented as P = ax + by.

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How do you find the vertex of a feasible region?

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Evaluate the objective function at each vertex of the feasible region to determine which gives the maximum or minimum value.

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What is the substitution method for solving systems of equations?

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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 elimination method for solving systems of equations?

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A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.