Systems 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 a system of equations to have no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What is the elimination method in solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point into both equations; if both equations are true, it is a solution.

Front

What does it mean if two lines intersect at a point?

Back

The system of equations has exactly one solution, which is the point of intersection.

Front

What is the graphical representation of a system with infinitely many solutions?

Back

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

Front

How can you tell if a system of equations is consistent?

Back

If it has at least one solution, it is consistent.

Front

What is the first step in using the elimination method?

Back

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

Front

What is the solution to the system of equations: y = 2x + 3 and y = -x + 1?

Back

(−2, −1)

Front

What does it mean for a system of equations to be inconsistent?

Back

It has no solutions, typically represented by parallel lines.