Question

Write a system of equations where the product of two numbers is 10 and the first number is 3 more than the second.
Can you determine the solution? Guess and check.
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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.