Question

write two numbers that multiply to the value on top and add to the value on
20
×
□ + □
9
answer attempt 1 out of 2

Explanation:

Step1: Define variables

Let the two numbers be \( x \) and \( y \). We know that \( x \times y = 20 \) and \( x + y = 9 \).

Step2: Solve the system of equations

From \( x + y = 9 \), we can express \( y = 9 - x \). Substitute this into the multiplication equation: \( x(9 - x)=20 \).
Expand to get \( 9x - x^{2}=20 \), rearrange to \( x^{2}-9x + 20 = 0 \).
Factor the quadratic equation: \( (x - 4)(x - 5)=0 \).
So \( x = 4 \) or \( x = 5 \). If \( x = 4 \), then \( y = 9 - 4 = 5 \); if \( x = 5 \), then \( y = 9 - 5 = 4 \).

Answer:

The two numbers are 4 and 5 (or 5 and 4).