Systems of Linear Equations (Classic)

- Adjust the numerical values into the equations and observe the effect on the graphs of the two lines.
- Adjust the numerical values until the two lines intersect and record the
point of intersection (mouse over the point to see its coordinates).
- What happens if you multiply the first equation by 2? (Double each coefficient and the right-hand-side.) Explain.
- Predict what will happen to the graph and the intersection point if we replace the second equation with the sum of the two equations. Try it.
- Make some conjectures based on what you have observed.

- Create a system of equations that has no solution (no intersection point).
- What do you observe about the slopes of the two lines?

- Create a system of equations that has infinitely many solutions.
- What is different about the two lines in this case as compared to the "no solution" case?

- Turn on the "show determinant" option and observe the value of the
determinant as you create systems with one solution, no solutions, or
infinitely many solutions.
- Conjecture how you might use the determinant to give you information on the number of solutions a linear system has.