Question

Katie was asked to plot two lines of equation 3x-y=2 and y+kx=1 where k is constant. Find all possible values of k that will satisfy each of the following conditions. Explain the reasons for your choice. (I) The two lines have 1 solution at (2,4). (II) The two lines have no solution. (III) The two lines have an infinite number of solutions.

Answer 1

Answer:

If we end up with the same term on both sides of the equal sign, such as 4 = 4 or 4x = 4x, then we have infinite solutions. If we end up with different numbers on either side of the equal sign, as in 4 = 5, then we have no solutions.