Question

What are 2 numbers that have a sum of 9 and their difference is 5?

Answer 1

Given :-

The sum of two numbers is 9

and their difference is 5

TO FIND

The two numbers

A.T.Q :-

Let the number be x and y

So

$\sf \:\:\: x+y=9------(i)\\ \\ \sf\:\:\: x-y=5------(ii)\\ \\ \sf\implies x=5+y\\ \\ \sf\:\:\: substitute\:the\:value\:of\: x\:in\:eq.. (i) \\ \\ \sf\implies 5+y+y=9\\ \\ \sf\implies 2y=9-5\\ \\ \sf\implies 2y=4\\ \\ \sf\implies y= \cancel{\dfrac{4}{2}}\\ \\ \sf\implies y=2$

So the value of y is 2

Now find the value of x

$\sf\implies x+y=9\\ \\ \sf\implies x+2=9\\ \\ \sf\implies x=9-2\\ \\ \sf\implies x=7$

$\boxed{\sf{x=7\:\:and\:\:y=2}}$

The two numbers is 7 and 2

Answer 2

Answer:

The two numbers are 7 and 2

Step-by-step explanation:

Given:

Sum of two numbers = 9

Difference of the same 2 numbers = 5

Assumption:

Let the first number be = X

Let the second number be = Y

According to the question,

The sum is 9 : X + Y = 9 - - - - - - - (1)

The difference is 5 : X - Y = 5 - - - - - - -(2)

Adding equations (1) and (2), we get:

( X + Y + X - Y) = 9 + 5

(2X) = 14

$x = \frac{14}{2}$

X = 7

Substituting the value of X in equation 1, we get:

( 7 + Y ) = 9

Y = 9 - 7

Y = 2

The two numbers are 7 and 2

Verify:

Substituting these values in equation (2), we get :

( 7 - 2 ) = 5

5=5

L.H.S = R.H.S

Hence verified