Systems Intro

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 two lines intersect on a graph?

Back

It means the system of equations has one unique solution.

Front

What does it mean if two lines are parallel on a graph?

Back

It means the system of equations has no solution.

Front

What does it mean if two lines are the same on a graph?

Back

It means the system of equations has infinitely many solutions.

Front

How can you find the solution to a system of equations graphically?

Back

By plotting the lines on a graph and identifying their intersection point.

Front

What is the solution to the system of equations represented by the lines y = 2x + 1 and y = -x + 4?

Back

(1, 3) - The lines intersect at this point.

Front

If a system of 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 graphical representation of a system with no solutions?

Back

Two parallel lines that never intersect.

Front

What is the significance of the point (4, 3) in a system of equations?

Back

It represents a solution where both equations are satisfied.

Front

How do you determine if a system of equations has one solution?

Back

Check if the lines intersect at exactly one point.