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 point(s) where the equations intersect.

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What does it mean for an ordered pair to be a solution of a system of equations?

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An ordered pair (x, y) is a solution of a system of equations if it satisfies all equations in the system when substituted for x and y.

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How do you determine if an ordered pair is NOT a solution?

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To determine if an ordered pair is NOT a solution, substitute the values of the ordered pair into each equation. If it does not satisfy at least one equation, it is not a solution.

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What is the graphical representation of a linear equation?

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The graphical representation of a linear equation is a straight line on a coordinate plane, where each point on the line represents a solution to the equation.

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What is the difference between a system of equations and a system of inequalities?

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A system of equations consists of equations that are equal, while a system of inequalities consists of inequalities that define a range of possible solutions.

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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 make all equations true simultaneously.

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What are the common methods to solve systems of equations?

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Common methods include graphing, substitution, and elimination.

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What is the substitution method?

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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?

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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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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 write them as a system.