Systems of Equations 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 combining equations to eliminate one variable.

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 an infinite number of solutions?

Back

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

Front

How do you determine if a system of equations has one solution?

Back

If the lines represented by the equations intersect at exactly one point.

Front

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

Back

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

Front

How can you manipulate equations to use the elimination method?

Back

You can multiply one or both equations by a constant to align coefficients for elimination.

Front

What is the solution to the system: 3x + 7y = 23 and -3x - 7y = -17?

Back

No solution.

Front

What is the solution to the system: 4x + 8y = 20 and -4x + 2y = -30?

Back

(7, -1).