Question

The sum of two numbers, x and y, is 12. The difference of x and two times y is 6. What are the values of x and y?

Answer 1

The values of x= 10 and y = 2

Explanation:

Assume
`x>y`

The first statement states that sum of two numbers, x and y, is 12

then, we can write this statement in algebraic expression:

`x+y =12` ...[1]

The second statement states that the difference of x and two times y is 6.

we can write it as :

`x -2y =6` ....[2]

Now, subtracting equations, we will eliminate x leaving an equation in y that we can solve:

⇒ [1]-[2] gives

`(x+y)-(x-2y) = 12-6`

or

`x+y-x+2y = 6`

On simplify we get;

3y=6 or

y=2

Now, substitute the value of y=2 in equation [1] we get;

`x+2=12`

On simplify, we get;

x =10

therefore, the values of x and y are, 10 and 2.

Answer 2

We write to expressions since there are two unknown here which is x and y. The first expression is the sum of two numbers, x and y, is 12.

x + y = 12

The second expression is that the difference of x and two times y is 6.

x -2y = 6

Therefore, the values of x and y are 10 and 2.