System of Linear Equations Elimination

Front

What is a system of linear equations?

Back

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

Front

What does it mean for two lines to be parallel in a system of linear equations?

Back

Parallel lines do not intersect and have no solutions.

Front

What does it mean for two lines to intersect in a system of linear equations?

Back

Intersecting lines have exactly one solution, which is the point of intersection.

Front

What does it mean for two equations to represent the same line?

Back

They have infinitely many solutions, as every point on the line is a solution.

Front

How can you solve a system of linear equations using the elimination method?

Back

By adding or subtracting the equations to eliminate one variable, then solving for the other.

Front

What is the solution to the system -4x - 2y = -12 and 4x + 8y = -24?

Back

(6, -6)

Front

If a system of linear equations has no solution, what can be said about the lines?

Back

The lines are parallel.

Front

If a system of linear equations has one solution, what can be said about the lines?

Back

The lines intersect at exactly one point.

Front

If a system of linear equations has infinitely many solutions, what can be said about the lines?

Back

The lines are coincident, meaning they lie on top of each other.

Front

What is the elimination method?

Back

A technique for solving systems of equations by eliminating one variable to solve for the other.