18. One number is 3 less than a second number. Twice the second number is 12 more than 3 times the first.

Find the two numbers.

Answer: The numbers are - 3 and - 6

Step-by-step explanation:

Let the first number be x and the second number be y, then from the first statement we have

x + 3 = y ... equation 1

From the second statement

2y = 3x + 12 ... equation 2

solving the resulting simultaneous equation by substitution method, we have:

substitute x - 3 = y into equation 2, we have

2 (x + 3) = 3x + 12

2x + 6 = 3x + 12

2x - 3x = 6

x = - 6

substitute x = - 6 into equation 1, that is

- 6 + 3 = y

Therefore,

y = - 3

2y = 3y + 3

Check:

x + 3 = y, implies

-6 + 3 = - 3 = y

Also 2y = 3x + 12, implies

2 (-3) = - 6

3 (-6) + 12 = - 6