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 lines representing the equations are the same line, meaning they overlap completely.

Front

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

Back

By analyzing the graphs of the equations: if they intersect at one point, there is one solution; if they are parallel, there is no solution; if they are the same line, there are infinite solutions.

Front

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

Back

No Solution (the lines are parallel).

Front

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

Back

(1, 3) (the lines intersect at this point).

Front

What does it mean for two lines to intersect at a point?

Back

It means that there is one unique solution to the system of equations.

Front

If two lines are parallel, what can be said about their slopes?

Back

The slopes of parallel lines are equal.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the graphs of the equations on a coordinate plane.

Front

What is the significance of the point of intersection in a system of equations?

Back

It represents the solution to the system, where the values of the variables satisfy all equations.