Solving Systems of Equations

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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 to the system is the set of values that satisfy all equations simultaneously.

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What are the methods to solve a system of equations?

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The main methods to solve a system of equations are: 1) Graphing, 2) Substitution, 3) Elimination.

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How do you use the substitution method to solve a system of equations?

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To use the substitution method, solve one equation for one variable, then substitute that expression into the other equation to find the values of the variables.

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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 does it mean for a system of equations to be consistent?

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A consistent system of equations has at least one solution, meaning the equations intersect at one or more points.

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What does it mean for a system of equations to be inconsistent?

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An inconsistent system of equations has no solutions, meaning the equations represent parallel lines that never intersect.

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What is a dependent system of equations?

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A dependent system of equations has infinitely many solutions, meaning the equations represent the same line.

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How do you graph a system of equations?

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To graph a system of equations, plot each equation on the same coordinate plane and identify the point(s) where the lines intersect.

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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 (if necessary) so that adding or subtracting them will eliminate one variable.