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
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.