Question

The sum of two numbers is 12. their difference is 2. find the numbers

Answer 1

let x represent the first number=5
let y represent the second number =7
x+y=12 x+y=12 x+7=12
-1(x-y=2) + -x+y=-2 -7 -7
----------- -----------
0+2y=14 x=5
--------- Y=7
2 2

Answer 2

The numbers are 7 and 5.

Explanation:

Let two unknown numbers be x and y .

Assume
`x>y`.

The first expression is given : The sum of two numbers is 12.

we have,

x+y =12 ...[1]

The second expression states that : The difference of two numbers is 2 , i.e,

we have;

x- y =2 .....[2]

Now, adding the equations, term by term on both sides, we will eliminate y leaving an equation in x that we can solve:

then, [1]+[2] gives

`x+y+x-y = 12 +2`

Simplify we get;

`2x = 14`

⇒
`x= 7`

Substitute the value of x =7 in equation [1];

`7+y =12`

On simplify, we get;

y = 5.