Final answer:
To find the two numbers, we can set up two equations and solve for the variables. The numbers are -69 and -60.
Step-by-step explanation:
To find the two numbers, let's represent them as x and y. According to the problem, one number is nine less than the other, so we can write the equation: x = y - 9. Additionally, five times the first number is 15 more than six times the second number, so we can write the equation: 5x = 6y + 15.
To solve these equations, we can substitute the value of x from the first equation into the second equation. Substituting y - 9 for x, we get 5(y - 9) = 6y + 15. Simplifying this equation gives us 5y - 45 = 6y + 15. By moving the variables to one side and the constants to the other side, we get y - 6y = 15 + 45, which simplifies to -y = 60.
Dividing both sides of the equation by -1, we find that y = -60. Substituting this value back into the first equation x = y - 9, we find x = -60 - 9 = -69. Therefore, the two numbers are x = -69 and y = -60.