Solving Systems - Graphing

Front

What is the solution to the system of equations represented by the intersection of two lines?

Back

The solution is the point where the two lines intersect.

Front

If two lines are graphed and they intersect at (4, -2), what does this point represent?

Back

This point represents the solution to the system of equations.

Front

What does it mean if two lines are graphed and they are parallel?

Back

It means the system has no solution.

Front

What does it mean if two lines are graphed on top of each other?

Back

It means the system has infinitely many solutions.

Front

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

Back

By analyzing the graphs of the equations: intersecting lines have one solution, parallel lines have no solution, and coincident lines have infinitely many solutions.

Front

What is the graphical representation of the equation 3x + 2y = 16?

Back

It is a straight line on a coordinate plane.

Front

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

Back

By plotting both equations on the same graph and identifying the intersection point.

Front

What is the solution to the system of equations 3x + 2y = 16 and 7x + y = 19?

Back

The solution is (2, 5).

Front

What does the term 'no solution' indicate in a system of equations?

Back

It indicates that the lines representing the equations do not intersect.

Front

What does the term 'infinitely many solutions' indicate in a system of equations?

Back

It indicates that the lines representing the equations are the same line.