Systems of Linear Equations (Two Variables)

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 if a system of linear equations has no solution?

Back

The lines represented by the equations are parallel and never intersect.

Front

What does it mean if a system of linear equations has infinite solutions?

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

How is a solution to a system of linear equations represented?

Back

As an ordered pair (x, y) that satisfies all equations in the system.

Front

What is the graphical representation of a system of linear equations?

Back

It is represented by the intersection points of the lines on a coordinate plane.

Front

What is the substitution method in solving systems of linear equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of linear equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

Solve the system: y = x + 3 and -2x + 2y = 6.

Back

Infinite solutions.

Front

Solve the system: 3x - 4y = 14 and 5x + y = 8.

Back

(2, -2).

Front

Solve the system: y = -4x + 5 and 2x - 3y = 13.

Back

(2, -3).