Math Problem Statement
Is it possible for two numbers to have a difference of 8, and a sum of 1?
Solution
Yes, it is possible for two numbers to have a difference of 8 and a sum of 1. Let’s solve for the two numbers step by step.
Let the two numbers be and .
From the problem:
-
The difference of the two numbers is :
-
The sum of the two numbers is :
Step 1: Solve the system of equations.
We have:
Add the two equations to eliminate :
Substitute into one of the equations (e.g., Equation 2):
Final Answer:
The two numbers are:
Verification:
- Difference: ✅
- Sum: ✅
Do you want a more detailed breakdown of the steps or have further questions?
Related Questions:
- Can two numbers have the same difference and sum?
- How would the solution change if the sum was negative?
- What happens if the difference and sum are equal?
- Can we solve similar problems using a graph?
- How are such problems applied in real-life scenarios?
Tip:
For problems involving a sum and difference, adding and subtracting the equations simplifies finding the values of the variables!
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Math Problem Analysis
Mathematical Concepts
Algebra
Systems of Equations
Linear Equations
Formulas
x - y = 8
x + y = 1
Theorems
System of linear equations (solving by addition/subtraction)
Suitable Grade Level
Grades 7-9
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