the sum of two numbers is 186 the difference between the same numbers is 32. create a system of equations to model the situation

x + y = 186

x - y = 32

therefore x = 109

y = 77

Step-by-step explanation:

let the two numbers be x and y

sum of the two numbers equals 186 implies that

x + y = 186 ... eqn 1

the difference between the same numbers is 32 implies that

x - y = 32 ... eqn 2

from equation 2

x - y = 32

x = 32 + y ... eqn 3

substitute for x = 32 + y in equation 1

x+y = 186

32 + y + y = 186

32 + 2y = 186

2y = 186-32

2y = 154

divide both sides by 2

2y/2 = 154

y = 77

put y = 77 in equation 3

x = 32 + y ... eqn 3

x = 32 + 77

x = 109

check if your answer is correct

from x + y = 186

109 + 77 = 186

186 = 186 ... proved