Question

he numbers x and y satisfy both of the equations 23 x + 977 y = 2023 and 977 x + 23 y = 2977 What is the value of x 2 − y 2 ?

Answer 1

5

Explanation:

23 x + 977 y = 2023

977 x + 23 y = 2977

add the 2 together

1000x+1000y =5000

so x+y =5

x=5-y

plug this into first equation

23(5-y) +977y =2023

solve for y =2

so x=3

x² -y² =(x+y)*(x-y) =5*1 =5