Question

Find two numbers with a sum of 104 and a difference of 42

Answer 1

`a=73 \text{ and } b=31`

Explanation:

`a+b=104 --- (1)\\a-b=42 ---(2)\\`

Add (1) and (2), we get

`2a=104+42\\a=(146)/(2)\\=73`

`73-b=42\\-b=42-73\\b=31`

Answer 2

31 and 73

Explanation:

Writing this is variable form,

x+y = 104

x-y = 42

If we use the process of elimination and add the system of equations together;

2x = 146

x = 73

Substituting that back in;

x - y = 42

(73) - y = 42

y = 31