System of Equations Using Elimination P1-2

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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 it mean to solve a system of equations using elimination?

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Solving a system of equations using elimination involves adding or subtracting the equations to eliminate one variable, making it easier to solve for the other variable.

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What is the first step in the elimination method?

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The first step is to align the equations so that the coefficients of one of the variables are opposites or can be made opposites.

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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 adding or subtracting the equations after multiplying one or both equations by a suitable number.

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What is the solution to the system of equations 2x + 3y = 6 and 4x + 6y = 12?

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The solution is (0, 2). This system has infinitely many solutions because the second equation is a multiple of the first.

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

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A system of equations has no solution if the lines represented by the equations are parallel and 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 of equations has infinitely many solutions if the equations represent the same line, meaning they intersect at every point on that line.

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Solve the system using elimination: 2x + 3y = 6 and 2x - y = 4. What are x and y?

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x = 2, y = 0.

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What is the elimination method used for?

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The elimination method is used to find the values of variables in a system of equations by eliminating one variable at a time.

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What is a key advantage of using the elimination method?

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A key advantage is that it can be more straightforward than substitution, especially when dealing with larger systems.