Solving Systems of Equations

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What is a system of equations?

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A set of two or more equations with the same variables that are solved together.

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

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It means that the equations represent parallel lines that never intersect.

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What is the solution to a system of equations?

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The point(s) where the equations intersect, representing the values of the variables that satisfy all equations.

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What is the graphical representation of a system of equations?

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It is represented by lines or curves on a coordinate plane.

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

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It means that the equations represent the same line, and every point on that line is a solution.

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How do you solve a system of equations using substitution?

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Solve one equation for one variable and substitute that expression into the other equation.

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How do you solve a system of equations using elimination?

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Add or subtract the equations to eliminate one variable, making it easier to solve for the other.

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

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Identify the method you will use: substitution, elimination, or graphing.

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What is the importance of checking your solution in a system of equations?

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To ensure that the solution satisfies all equations in the system.

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What is the elimination method?

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A method for solving systems of equations by adding or subtracting equations to eliminate a variable.