Solving Systems Using Elimination

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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 determine if a point is a solution to a system of equations?

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Substitute the point's coordinates into both equations. If both equations are satisfied, the point is a solution.

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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 that are solved simultaneously.

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What does it mean for two equations to be consistent?

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Two equations are consistent if they have at least one solution.

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What does it mean for two equations to be independent?

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Two equations are independent if they have exactly one solution.

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What does it mean for two equations to be dependent?

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Two equations are dependent if they represent the same line, meaning they have infinitely many solutions.

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How do you eliminate a variable in a system of equations?

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You can eliminate a variable by multiplying one or both equations by a number so that the coefficients of one variable are opposites, allowing for cancellation when the equations are added or subtracted.

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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 decide which variable to eliminate.

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The solution is any point on the line, as the equations are dependent.

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The solution is (0, 4).