3 Variable Linear Systems of Equations

Front

What is a system of linear equations?

Back

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

Front

What does it mean if a system of equations has no solution?

Back

It means that the equations represent parallel lines that never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

It means that the equations represent the same line, leading to an infinite number of intersection points.

Front

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

Back

The graphical representation consists of lines on a coordinate plane, where the intersection point(s) represent the solution(s).

Front

What is the substitution method in solving linear equations?

Back

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

Front

What is the elimination method in solving linear equations?

Back

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

Front

What does it mean if you encounter the statement 0=4 when solving a system of equations?

Back

It indicates that the system has no solutions.

Front

What does it mean if you encounter the statement 0=0 when solving a system of equations?

Back

It indicates that the system has infinitely many solutions.

Front

What is a consistent system of equations?

Back

A system that has at least one solution.

Front

What is an inconsistent system of equations?

Back

A system that has no solutions.