System of Equations Graphs

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

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

Front

What is the graphical representation of a system of equations?

Back

It is the intersection point(s) of the lines representing the equations.

Front

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

Back

By analyzing the slopes and y-intercepts of the lines: parallel lines (no solution), same line (infinite solutions), or intersecting lines (one solution).

Front

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

Back

No Solution (the lines are parallel).

Front

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

Back

One Solution: (1, 3).

Front

What is the solution to the system of equations y = 3x + 1 and y = 3x + 5?

Back

No Solution (the lines are parallel).

Front

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

Back

Infinite Solutions (the equations are the same line).

Front

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

Back

It means the system of equations has one unique solution at that point.