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 elimination mean in the context of systems of equations?

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

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

Back

Identify which variable can be eliminated by adding or subtracting the equations.

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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 manipulating the equations (e.g., multiplying one or both equations) so that when added or subtracted, one variable cancels out.

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What is the solution to a system of equations?

Back

The solution is the point (x, y) where the graphs of the equations intersect.

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

Back

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?

Back

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

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

Back

Substitute the solution back into the original equations to see if both equations are satisfied.

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(1, 1)

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(10, -9)