Question

Plug a few points into the original equations and check to show that the system of

equations has one solution. Explain your work
3x+18=5x+8
4x + 22 = 8x + 10

Answer 1

[AI-generated answer — Bot GPT 3.5]

First, let's solve the first equation: 3x + 18 = 5x + 8

3x + 18 = 5x + 8
Subtract 3x from both sides:
18 = 2x + 8
Subtract 8 from both sides:
10 = 2x
Divide by 2:
5 = x

Now that we have found the value of x, let's plug it into the second equation to verify that it holds true for the system:

4(5) + 22 = 8(5) + 10
20 + 22 = 40 + 10
42 = 50

This statement is not true, which means that the system does not have one solution. We made an error in our calculations, or there could potentially be an issue with the original equations.

Answer 2

Plug a few points into the original equations and check to show that the system of

equations has one solution. Explain your work
3x+18=5x+8

Answer 3

[AI-generated answer — Bot GPT 3.5]

Let's solve the equation 3x + 18 = 5x + 8 to check if the system of equations has one solution.

3x + 18 = 5x + 8
Subtract 3x from both sides:
18 = 2x + 8
Subtract 8 from both sides:
10 = 2x
Divide by 2:
5 = x

Now that we have found the value of x, let's substitute x back into the original equation and see if both sides are equal:

3(5) + 18 = 5(5) + 8
15 + 18 = 25 + 8
33 = 33

Since both sides are equal, we have verified that x = 5 is the correct solution for the given system of equations. Therefore, the system of equations has one solution.

Answer 4

Plug a few points into the original equations and check to show that the system of

equations has one solution. Explain your work
4x + 22 = 8x + 10

Answer 5

[AI-generated answer — Bot GPT 3.5]

To determine if the system of equations has one solution, we need to solve the equation 4x + 22 = 8x + 10.

4x + 22 = 8x + 10
Subtract 4x from both sides:
22 = 4x + 10
Subtract 10 from both sides:
12 = 4x
Divide by 4:
3 = x

Now, substitute x = 3 back into the original equation to check for consistency:

4(3) + 22 = 8(3) + 10
12 + 22 = 24 + 10
34 = 34

Since both sides are equal, x = 3 is the correct solution for the given system of equations. Therefore, the system has one solution.