Solving Systems of Equations using 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 point(s) where the equations intersect.

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What does elimination mean in the context of solving systems of equations?

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Elimination is a method used to solve systems of equations by removing one variable, allowing for the solution of the remaining variable.

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

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To eliminate a variable, you can add or subtract the equations in such a way that one variable cancels out.

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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 so that the coefficients of one variable are opposites or can be made opposites.

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If you have the equations 2x + 3y = 6 and 4x + 6y = 12, what can you conclude?

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The two equations represent the same line, so there are infinitely many solutions.

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

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Checking your solution ensures that the values satisfy all equations in the system, confirming that the solution is correct.

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What is a common mistake when using elimination?

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A common mistake is incorrectly adding or subtracting the coefficients, leading to an incorrect equation.

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How can you make the coefficients of a variable opposites in elimination?

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You can multiply one or both equations by a number to create opposite coefficients for the variable you want to eliminate.

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

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A system has no solution if the equations represent parallel lines that never intersect.

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

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A system has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.