Question

The sum of two numbers is 32. The difference between the numbers is 8. Write a system of equations to represent this situation. Then solve the system of equations by substitution. Explain what the solution means

Answer 1

`Let\: x,y\: (x>y>0) \: be \: the \: two \: numbers.\\We \: have \: an \: equality:\\\begin{cases} x + y = 32\\x - y = 8 \end{cases}\\ \Leftrightarrow \begin{cases} 2x = 40\\y = x - 8 \end{cases} \\ \Leftrightarrow \begin{cases} x = 20\\y = 20 - 8 = 12 \end{cases} \\ \Rightarrow The \: two \: numbers \: are \: 2 0 \: and \: 12`