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.

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 elimination method?

Back

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

Front

How do you determine if a system of equations has no solution?

Back

If the equations represent parallel lines, they have no solution because they 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, and every point on that line is a solution.

Front

What is the first step in the elimination method?

Back

Align the equations so that corresponding variables and constants are in the same columns.

Front

How can you make the coefficients of one variable the same in both equations?

Back

You can multiply one or both equations by a suitable number.

Front

What is the purpose of adding or subtracting the equations in the elimination method?

Back

To eliminate one variable, making it possible to solve for the other variable.

Front

What do you do after finding the value of one variable?

Back

Substitute that value back into one of the original equations to find the value of the other variable.

Front

What is a consistent system of equations?

Back

A system that has at least one solution.