Solving Systems of Equations by Elimination

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean to solve a system of equations by elimination?

Back

It means to eliminate one variable by adding or subtracting the equations, allowing you to solve for the other variable.

Front

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

Back

Get both equations in standard form and line up the like terms.

Front

How do you represent a word problem as a system of equations?

Back

Identify the variables, write equations based on the relationships described, and ensure they reflect the problem's conditions.

Front

What is the standard form of a linear equation?

Back

Ax + By = C, where A, B, and C are constants.

Front

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

Back

Substitute the values of the variables back into the original equations to see if they hold true.

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What is the elimination method?

Back

A method for solving systems of equations by adding or subtracting equations to eliminate one variable.

Front

What is the significance of lining up like terms in elimination?

Back

It helps to easily identify which terms can be eliminated when adding or subtracting the equations.

Front

If you have the equations 2x + 3y = 12 and 5x - y = 13, what is the first step to solve by elimination?

Back

Multiply the second equation by 3 to align the y terms for elimination.

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What is the solution to the system of equations 4x + 4y = 4 and 3x + 4y = 10?

Back

(-6, 7) is the solution.