Exercise 4 Page 268

Let's begin by considering the possibilities for the boxes.

1. The boxes hold the same number
2. The boxes hold different numbers.

If we fill each box with the same number, we get an equation where the left- and right-hand sides are identical. Let's use the number 2. 4x+2=4x+2 When we graph each side of the equation, we get two overlapping lines and as such, there are infinitely many solutions.

If we fill each box with different numbers, we will get parallel lines. Notice that in this case, the left- and right-hand sides are not equal. Let's fill the first box with 3 and the second box with 1. 4x+3 ≠ 4x+1 As the lines are parallel, they will never intersect. This means there are no solutions.

We can conclude that our friend is incorrect.