Solving Systems of Equations using Elimination

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What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is the elimination method?

Back

A technique for solving systems of equations by adding or subtracting equations to eliminate a variable.

Front

When is it best to use the elimination method?

Back

When the coefficients of one variable are opposites or can be easily manipulated to become opposites.

Front

What does it mean if two lines are parallel in a system of equations?

Back

They have the same slope and will never intersect, indicating no solution.

Front

What is an infinite solution in a system of equations?

Back

When the equations represent the same line, resulting in an unlimited number of solutions.

Front

What is a no solution scenario in a system of equations?

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When the equations represent parallel lines that never intersect.

Front

How do you determine which variable to eliminate first?

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Choose the variable that has coefficients that are easiest to manipulate to become opposites.

Front

What is the first step in the elimination method?

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Align the equations so that like terms are in the same column.

Front

What happens when you add two equations with opposite coefficients for one variable?

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The variable with opposite coefficients cancels out, allowing you to solve for the other variable.