Question

write two numbers that multiply to the value on top and add to the value on bottom.
18
×

+
9
answer
attempt 1 out of 10

Explanation:

Step1: Define variables

Let the two numbers be \( x \) and \( y \). We have two equations: \( xy = 18 \) and \( x + y = 9 \).

Step2: Solve the system of equations

From \( x + y = 9 \), we can express \( y = 9 - x \). Substitute into \( xy = 18 \):
\( x(9 - x)=18 \)
\( 9x - x^{2}=18 \)
\( x^{2}-9x + 18 = 0 \)

Step3: Factor the quadratic equation

Factor \( x^{2}-9x + 18 \):
\( x^{2}-9x + 18=(x - 3)(x - 6)=0 \)
So \( x = 3 \) or \( x = 6 \). If \( x = 3 \), then \( y = 9 - 3 = 6 \); if \( x = 6 \), then \( y = 9 - 6 = 3 \).

Answer:

3 and 6 (or 6 and 3)