Final answer:
To solve the equation, assume the smaller number is x and the greater number is y. Substitute the value of y into the equation and simplify to find x. Use the first equation to find the value of y. The two numbers are 29 and 34.
Step-by-step explanation:
To solve the equation, let's assume the smaller number is x and the greater number is y.
We are given that the two numbers differ by 5, which can be written as:
y = x + 5
We are also given that 3 less than four times the smaller number minus 3 times the greater number is 11, which can be written as:
4x - 3y - 3 = 11
Substituting the value of y from the first equation into the second equation:
4x - 3(x + 5) - 3 = 11
Simplifying the equation:
x - 18 = 11
Adding 18 to both sides of the equation:
x = 29
So the smaller number is 29. Using the first equation, we can find the value of y:
y = x + 5 = 29 + 5 = 34
Therefore, the two numbers are 29 and 34.