Systems of Equations - Substitution and Elimination

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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?

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To solve a system of equations means to find the values of the variables that make all equations in the system true.

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What is the substitution method in solving systems of equations?

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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 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 other variable.

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How do you isolate a variable in an equation?

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To isolate a variable, you perform inverse operations to get the variable on one side of the equation and all other terms on the opposite side.

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

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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 using elimination to solve a system of equations?

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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.

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

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