1. The two lines ╥3x + 5y = 7╙ and ╥3.01x + 5y = 10╙ are almost parallel, but not quite. What do you think would happen if you plotted both of these lines on the same coordinate system? Would they intersect? Would the intersection be close to the origin or far away?
2. A linear equation of the form Ax + By = 0 (that is, where the constant term is zero) is called a HOMOGENEOUS linear equation. What is one point in the xy-plane that is always a solution of any homogeneous linear equation?
3. Does a system consisting of two different homogeneous linear equations always have a solution? If so, what is it?
4. If the graphs of two lines are perpendicular, does the system consisting of the equations of the two lines always have a solution?
5. If you graph a system of THREE linear equations, what are some of the ways the three lines could look? How would they look if the system had a solution? How would they look if no two of them were parallel, but the system had no solution?
