Question

If x+y = z and y−z=x which of the following must be equal to z?

(A) 0 (B) x (C) y (D) −x (E) –y

Answer 1

(C) y

Step-by-step explanation

We have two equations:

The first one is

`x + y = z...(1)`

The second equation is

`y - z = x...(2)`

Let us make z the subject of this second equation:

`\implies \: -x +y = z...(3)`

We now add equation (1) and (3) to get:

`(-x + x) + (y + y) = z + z`

We simplify to get:

`0+2y= 2z`

`2y= 2z`

Divide throu by 2.

`(2y)/(2) = (2z)/(2)`

`y= z`

`\therefore \: z = y`

The correct answer is C