Question

Plug more than one point into the original equations and check to show that the equations can have more than one solution. Explain your work.

Answer 1

Let's use the following equations as an example:

1. 2x + y = 4
2. x + 3y = 6

Now, let's plug in two different sets of values for x and y into the equations and see if they satisfy both equations:

Set 1:
1. x = 2, y = 0
2. 2(2) + 0 = 4 -> 4 = 4 (satisfied)
3. 2 + 3(0) = 6 -> 2 = 6 (not satisfied)

Set 2:
1. x = 1, y = 2
2. 2(1) + 2 = 4 -> 4 = 4 (satisfied)
3. 1 + 3(2) = 6 -> 7 = 6 (not satisfied)

As we can see, both sets of values satisfy the first equation but not the second equation. This shows that the equations can have more than one solution.