Final answer:
To solve this problem, we can set up a system of two equations using the given information. By solving this system using the substitution method, the two numbers are determined to be 4 and -1.
Step-by-step explanation:
To solve this problem, let's assign variables to the two numbers. Let x be the greater number and y be the lesser number.
The first piece of information tells us that the difference of two numbers is five, so we can write the equation: x - y = 5.
The second piece of information tells us that five times the lesser number minus the greater number is -9, so we can write the equation: 5y - x = -9.
Now we have a system of two equations with two variables. We can solve this system using a method like substitution or elimination to find the values of x and y.
Let's use the substitution method:
From the first equation, we can rewrite it as x = y + 5.
Substitute this expression for x in the second equation:
5y - (y + 5) = -9
Simplify the equation:
4y - 5 = -9
Add 5 to both sides:
4y = -4
Divide both sides by 4:
y = -1
Substitute this value back into the first equation:
x - (-1) = 5
x + 1 = 5
Subtract 1 from both sides:
x = 4
So the two numbers are 4 and -1.