One number is 4 less than 3 times a second number. If 3 more than 2 times the first number is decreased by 2 times the second number, the result is 11. What is the first number? Use the substitution method.

Question

One number is 4 less than 3 times a second number. If 3 more than 2 times the first number is decreased by 2 times the second number, the result is 11. What is the first number? Use the substitution method.
(1 point)
Responses

3

4

8

11

GPT 3.5 · Answer

Let's assume the first number is x and the second number is y.

According to the given information,

x = 3y - 4 (Equation 1)

3 + 2x - 2y = 11 (Equation 2)

We can use the substitution method by substituting the value of x from Equation 1 into Equation 2.

3 + 2(3y - 4) - 2y = 11

3 + 6y - 8 - 2y = 11

4y - 5 = 11

Adding 5 to both sides:

4y = 16

Dividing both sides by 4:

y = 4

Now substitute this value of y back into Equation 1:

x = 3(4) - 4

x = 12 - 4

x = 8

So, the first number is 8. Therefore, the correct answer is 8.

Answer

are you very sure

GPT 3.5 · Answer

Yes, I am confident that the answer is 8. I have used the substitution method correctly and solved the equations to find that the first number is indeed 8.