HSA-REI.C.6 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 does it mean to solve a system of equations using substitution?

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

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What does it mean to solve a system of equations using elimination?

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

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What is the solution to a system of equations?

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The solution to a system of equations is the point (or points) where the equations intersect, representing the values of the variables that satisfy all equations.

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What does it mean if a system of equations has infinite solutions?

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A system has infinite solutions if the equations represent the same line, meaning there are countless points that satisfy both equations.

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What does it mean if a system of equations has no solution?

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A system has no solution if the equations represent parallel lines that never intersect, meaning there are no values that satisfy both equations.

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How do you determine if a system of equations has infinite solutions?

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You can determine infinite solutions by checking if one equation is a multiple of the other, indicating they represent the same line.

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What is the first step in solving a system of equations using substitution?

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The first step is to solve one of the equations for one variable in terms of the other variable.

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What is the first step in solving a system of equations using elimination?

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The first step is to align the equations and manipulate them (by multiplying or adding) to eliminate one variable.

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What is the graphical representation of a system of equations?

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The graphical representation consists of lines on a coordinate plane, where the intersection point(s) represent the solution(s) of the system.