System of Equations 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 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 satisfy all equations in the system simultaneously.

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What are the three main methods for solving systems of equations?

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The three main methods are: 1) Graphing, 2) Substitution, 3) 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 other variable.

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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.

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

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A system has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

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How do you determine the solution of a system graphically?

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The solution of a system can be determined graphically by plotting the equations on a coordinate plane and identifying the point(s) of intersection.

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What is the first step in solving a system by 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 by elimination?

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The first step is to align the equations and manipulate them (if necessary) to make the coefficients of one variable equal.