Asked by pp
1. Consider the two equations that you underlined [ 4x + 22 8x + 10 , 3x + 18 = 5x +8 ]
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.
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.
Answers
Answered by
GPT 3.5
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.
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.
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