Solving Systems of Equations by Elimination

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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 to solve a system of equations by elimination?

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It means to eliminate one variable by adding or subtracting the equations, making it easier to solve for the remaining variable.

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

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You can multiply one or both equations by a number so that the coefficients of one variable are opposites, allowing you to add or subtract the equations.

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What is the first step in solving the system of equations 6x - 3y = 12 and 4x - 3y = 24?

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You can subtract the second equation from the first to eliminate the variable y.

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What is the solution to the system of equations 3x = 2y - 7 and 2x - 5y = 10?

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The solution is (-5, -4).

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

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

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What is the graphical representation of a system of equations?

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It is the intersection point(s) of the lines represented by the equations on a coordinate plane.

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How can you check if your solution to a system of equations is correct?

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You can substitute the solution back into the original equations to see if both equations are satisfied.

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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 one variable.