Enter values of A, B and C in the spreadsheet for the two equations your are trying to solve. After you have solved your system,

Click on the checkbox to reveal the solution.

- Find the solution to : 4x + 3y = 7 and 9x − 3y = 6. What do you notice about the blue equation in the applet?
- Find the solution to : 3x + 5y = −9 and 7x − 2y = 20. Does it matter if the values are switched between red and blue?
- Find the solution to : −3x + y = 16 and −4x − 2y = 18. What do you notice about the equations in the applet?
- Enter the following values Red: a=1, b=2, c=3 ; Blue a= 2, b= 4 and c=6.

What do you notice about the equations and the lines? How many solutions are there for this system? - Enter the following values Red: a=2, b=4, c=5; Blue a= −2, b= −4, c=10.

What do you notice about the equations and the lines? How many solutions does this system have? - Write three different systems yourself. One that has 1 solution, one that has 0 solutions and one that has infinitely many solutions. Solve and check your solutions.

S.H. Lapinski, November 13, 2008, Created with GeoGebra

Please direct questions and comments to HCPS Mathematics Specialist Henrico County Public Schools, 2009