Answer:
9 and 3
Step-by-step explanation:
The given relations can be used to write a system of equations for the two numbers.
Setup
Let the numbers be represented by x and y. The given relations can be written as ...
4x -5y = 21
3(x +y) = 36
Solution
We can divide the second equation by 3 and subtract x to find an expression for y.
x +y = 12 . . . . . . divide the second equation by 3
y = 12 -x . . . . . . subtract x
Substituting into the first equation, we get ...
4x -5(12 -x) = 21
9x -60 = 21 . . . . . . . simplify
9x = 81 . . . . . . . . . add 60
x = 9 . . . . . . . . . . divide by 9
y = 12 -9 = 3 . . . find y using the expression for it
The two numbers are 9 and 3.
