Write a system of equations where the product of two numbers is 10 and the first number is 3 more than the second.

Question

Can you determine the solution? Guess and check.
write short please dont put / |]{

Answer 1

Let the two numbers be \( x \) and \( y \). The system of equations can be written as:

1. \( xy = 10 \)
2. \( x = y + 3 \)

To solve using guess and check:

1. Substituting \( x \) in the first equation: \((y + 3)y = 10\) \(y^2 + 3y - 10 = 0\)

2. Factoring: \((y + 5)(y - 2) = 0\)

So, \( y = -5 \) or \( y = 2 \).

3. Finding \( x \):
   • If \( y = 2 \), then \( x = 5 \).
   • If \( y = -5 \), then \( x = -2 \).

Solutions:

• \( (5, 2) \)
• \( (-2, -5) \)

Both pairs satisfy the original conditions.