The sum of two numbers is 52. their difference is 9. write and solve system of equations to find the 2 numbers

Hey there :)

Let us first translate words into mathematics!

Sum of 2 numbers is 52
x + y = 52

Difference of 2 numbers is 9
x - y = 9

(eq.1)  x + y = 52
(eq.2) x - y = 9
Add both equations :   x + y = 52
                                   +  x - y = 9
                                         2x = 61
                                        x = 30.5
 We now have the value of x, substitute into eithe formulae to find y
x - y = 9 , 30.5 - y = 9 , 30.5 - 9 = y , 21.5 = y
x + y = 52 , 30.5 + y = 52 , 52 - 30.5 = y , 21.5 = y

x = 30.5
y = 21.5