Solving Systems by Elimination

Front

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 by elimination?

Back

It means to eliminate one variable by adding or subtracting the equations to find the value of the other variable.

Front

What is the elimination method?

Back

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

Front

What is a solution to a system of equations?

Back

A set of values for the variables that makes all equations true.

Front

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.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means the equations represent the same line, so there are countless points of intersection.

Front

How do you determine if two equations are equivalent?

Back

If one equation can be transformed into the other by multiplying or dividing by a non-zero number.

Front

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

Back

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

Front

What is the purpose of multiplying an equation in a system before elimination?

Back

To create coefficients that will allow one variable to be eliminated when the equations are added or subtracted.

Front

Solve by elimination: 2x + 3y = 6 and 4x + 6y = 12.

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Infinitely many solutions.