Question

The sum of two numbers is 95, and their difference is 61. What are the two numbers?

Answer 1

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

$x-y=61$

$78-y=61$

$y=78-61$

$\boxed{y=17}$

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

Answer 2

$\left \{ {x+y=95} \atop {x-y=61}} \right. \\ \\2x=156\\x= \frac{156}{2} \\ \\x=78\\ \\y=95-y\\y=95-78\\y=17$

First number 78, and the second is 17 .