1. Consider the two equations that you underlined [ 4x + 22 8x + 10 , 3x + 18 = 5x +8 ]

Question

2. What do you notice about these equations?
3. What does it mean to have one solution?
4. Plug a few points into the original equations and check to show that the system of
equations has one solution.

Answer 1

2. I noticed that both equations are in the form of ax + b = cx + d, where a, b, c, and d are constants.

3. Having one solution means that there is only one unique point of intersection between the two equations on a graph, meaning that the lines intersect at only one point.

4. Let's plug in a few points into the original equations:
- For the first equation:
When x = 1, 4(1) + 22 = 26
When x = 2, 4(2) + 22 = 30
- For the second equation:
When x = 1, 3(1) + 18 = 21
When x = 2, 3(2) + 18 = 24

Now, let's solve the system of equations:
4x + 22 = 3x + 18
4x - 3x = 18 - 22
x = -4

Plug x = -4 into one of the original equations:
4(-4) + 22 = -6
3(-4) + 18 = 6

Therefore, the system of equations has one solution at x = -4.