Final answer:
To find the smaller of two numbers with a sum of 11 and a difference of 21, we set up two equations from the given conditions and solve for the smaller number. The equations are x + y = 11 and x - y = 21. After combining and solving these equations, we find that the smaller number is -5.
Step-by-step explanation:
The question involves finding the smaller of two numbers given that their sum is 11 and their difference is 21. To solve this, we can set up two equations based on the information given:
- x + y = 11 (Equation for sum)
- x - y = 21 (Equation for difference)
To find the value of y (the smaller number), we can add both equations together:
x + y + x - y = 11 + 21
2x = 32
x = 16
Now we can substitute the value of x into the first equation to find y:
16 + y = 11
y = 11 - 16
y = -5
So, the smaller number is -5.