Question

the sum of two number 50 and their difference is 18 find the numbers​

Answer 1

let the numbers be X and Y

given

$x + y = 50 - - - i\\ x - y = 18 - - ii$

$substracting \: ii \: from \: i \\( x + y )-( x - y) = 50 - 18 \\ 2y = 32 \\ y = 16$

then x is

$50 - y \\ = 50 - 16 \\ = 34$

Answer 2

$\huge\mathbb{SOLUTION:-}$

Let the two numbers be a and b

$\sf\underline{\pink{\:\:\:\:\:\:\:Given:-\:\:\:\:\:\:\:\:\:\:}}$

$\sf\bullet a+b=50\:\:\:\:\:\:\:\:\:\:(i)\\ \\ \sf\bullet a-b=18\:\:\:\:\:(ii)$

• Now by adding equation (i) and (ii)

$\bf\underline{\red{\:\:\:\:\:\:\:A.T.Q:-\:\:\:\:\:\:\:}}$

$\sf:\implies (x+y)+(x-y)=50+18\\ \\ \sf:\implies x\cancel{+y}+x\cancel{(-y)}=68\\ \\ \sf:\implies 2x=68\\ \\ \sf:\implies x=\cancel{\dfrac{68}{2}}\\ \\ \sf:\implies x= 34$

$\sf\bullet {\blue{The\: value\: of \:x \:is \:34 }}$

• Now the value of y

$\sf\bullet x+y= 50\\ \sf:\implies \:\:x=34\\ \sf:\implies 34+y=50\\ \sf:\implies y= 50-34\\ \sf:\implies y=16$

$\boxed{\sf{The\:two\:numbers\:is\:\:34\:and\:16}}$