let

x = the first number

y = the second number

the sum of two numbers is 50

x + y = 50

the first number is 43 less than half of the second number

x = (y/2) - 43

the system of equations is

x + y = 50

x = (y/2) - 43

by substituting for x from the second into the first equation we get

(y/2) - 43 + y = 50

y/2 + 2y/2 = 50 + 43

3y/2 = 93 multiply both sides by 2

3y = 93*2 divide both sides by 3

y = 186/3

y = 62

x = 62/2 - 43 = 31 - 43 = -12

the numbers are 62 and -12.