Unit 8 - 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 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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How do you solve a system of equations using substitution?

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To solve by substitution, solve one equation for one variable, then substitute 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.

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What does it mean to find the solution of a system of equations?

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Finding the solution means determining the values of the variables that satisfy all equations in the system simultaneously.

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What is the graphical interpretation of a system of equations?

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The graphical interpretation involves plotting the equations on a coordinate plane; the solution is where the lines intersect.

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What is a consistent system of equations?

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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 is an inconsistent system of equations?

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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.

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How do you check the solution of a system of equations?

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To check the solution, substitute the values back into the original equations to see if they hold true.