INTRO Systems of Linear Equations

Front

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

Back

The system has no solution if the equations represent parallel lines that never intersect.

Front

What is the graphical representation of a system with infinite solutions?

Back

The graphical representation is two lines that coincide, meaning they are the same line.

Front

How can you determine the number of solutions in a system of linear equations?

Back

You can determine the number of solutions by analyzing the slopes and y-intercepts of the lines represented by the equations.

Front

What is the solution to the system of equations represented by the lines y = 2x + 1 and y = -x - 2?

Back

The solution is the point where the two lines intersect, which can be found by solving the equations simultaneously.

Front

What does it mean for two lines to be parallel in the context of linear equations?

Back

Two lines are parallel if they have the same slope but different y-intercepts, indicating they will never meet.

Front

What is the solution to the system of equations represented by the lines y = 3x + 4 and y = 3x - 2?

Back

The system has no solution because the lines are parallel.

Front

What is the significance of the point (1, -1) in a system of equations?

Back

The point (1, -1) is the solution to the system, meaning it is the point where the equations intersect.

Front

What is the significance of the point (-1, 2) in a system of equations?

Back

The point (-1, 2) is a solution to the system, indicating where the two lines intersect.

Front

What are the possible outcomes when solving a system of linear equations?

Back

The possible outcomes are one solution (intersecting lines), no solutions (parallel lines), or infinitely many solutions (coincident lines).

Front

How do you graphically represent a system of equations with one solution?

Back

You represent it with two lines that intersect at a single point.