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 xx and yy.

From the problem:

  1. The difference of the two numbers is 88: xy=8x - y = 8

  2. The sum of the two numbers is 11: x+y=1x + y = 1

Step 1: Solve the system of equations.

We have: xy=8(Equation 1)x - y = 8 \quad \text{(Equation 1)} x+y=1(Equation 2)x + y = 1 \quad \text{(Equation 2)}

Add the two equations to eliminate yy:

(xy)+(x+y)=8+1(x - y) + (x + y) = 8 + 1 2x=92x = 9 x=92=4.5x = \frac{9}{2} = 4.5

Substitute x=4.5x = 4.5 into one of the equations (e.g., Equation 2):

4.5+y=14.5 + y = 1 y=14.5y = 1 - 4.5 y=3.5y = -3.5

Final Answer:

The two numbers are: x=4.5andy=3.5x = 4.5 \quad \text{and} \quad y = -3.5

Verification:

  • Difference: 4.5(3.5)=4.5+3.5=84.5 - (-3.5) = 4.5 + 3.5 = 8
  • Sum: 4.5+(3.5)=14.5 + (-3.5) = 1

Do you want a more detailed breakdown of the steps or have further questions?

Related Questions:

  1. Can two numbers have the same difference and sum?
  2. How would the solution change if the sum was negative?
  3. What happens if the difference and sum are equal?
  4. Can we solve similar problems using a graph?
  5. 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!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

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