Question

I.The difference between two numbers is 5. Their product is 36.

A. Write two equations that model this situation.
B.What are the two numbers?

Answer 1

equ 1: X-Y=5
equ 2: x∗y=36
from Equ 1
X=5+Y------equ 3
substitute x=5+y in equ 2
(5+y)∗y=36
5y+y^2=36
y^2+5y-36=0
factorize by substitution
(y^2+9y)-(4y-36)=0
y(y+9)-4(y+9)=0
(y-4)(y+9)=0
y=4 or y=-9....

substitute y=4 or -9 in equ 1
x-4=5
x=5+4
x=9 OR

x-(-9)=5
x+9=5
x=5-9
x=-4

since -4∗-9=36
therefore y=-9 and x=-4