Question

The sum of two numbers is  95

, and their difference is  61 . What are the two numbers?

Answer 1

`\left \{ {x+y=95} \atop {x-y=61}} \right. \\ \\2x=156\\x= (156)/(2) \\ \\x=78\\ \\y=95-y\\y=95-78\\y=17`

First number 78, and the second is 17 .

Answer 2

Let's call:


`first\#=x`


`second\#=y`

then

when we have a SUM, we have PLUS and when we have a DIFFERENCE, we have MINUS... Let's go then...


`\begin{Bmatrix}x+y&=&95\\x-y&=&61\end{matrix}`

now we can sum all the rows then we got it... (This is the other way to solved this question)


`x+y+(x-y)=95+61`


`x+y+x-y=156`


`2x=156`


`\boxed{x=78}`

now we can replace this value at first or at second row, you just need to pick up one...

I'll choose the second one


`x-y=61`


`78-y=61`


`y=78-61`


`\boxed{y=17}`


`\boxed{\boxed{\begin{Bmatrix}x&=&78\\y&=&17\end{matrix}}}`