Solving Systems of Equations by Graphing

Front

What is a system of equations?

Back

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

Front

What does it mean for two lines to intersect on a graph?

Back

It means that the two equations have a common solution, represented by the point of intersection.

Front

How can you determine the solution to a system of equations by graphing?

Back

By plotting both equations on the same graph and identifying the point(s) where they intersect.

Front

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

Back

It indicates that the system of equations has no solutions, as the lines never intersect.

Front

What is the significance of the slopes of two lines in a system of equations?

Back

If the slopes are equal, the lines are parallel; if they are different, the lines will intersect at one point.

Front

What does it mean if two lines are graphed over each other?

Back

It means that the system of equations has infinitely many solutions, as every point on the line is a solution.

Front

How can you tell if a system of equations has one solution?

Back

If the two lines intersect at exactly one point, the system has one solution.

Front

What is the graphical representation of a system of equations?

Back

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

Front

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

Back

No solution, as 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), as the lines intersect at this point.