Which equation is equivalent to w=x+y−z ?

Question

z=w−x−y

z=x+y−w

z=(x+y)w

z=x+y+w

Answer 1

To determine which equation is equivalent to \( w = x + y - z \), we can rearrange this equation to solve for \( z \).

Starting with the original equation:

\[ w = x + y - z \]

We can add \( z \) to both sides:

\[ w + z = x + y \]

Now, subtract \( w \) from both sides to isolate \( z \):

\[ z = x + y - w \]

This matches one of the provided options. Rearranging it, we can also express it as:

\[ z = x + y - w \]

To see which option this corresponds to, let's look at the given options:

1. \( z = w - x - y \) (not equivalent)
2. \( z = x + y - w \) (this matches)
3. \( z = (x + y)w \) (not equivalent)
4. \( z = x + y + w \) (not equivalent)

Thus, the equation that is equivalent to \( w = x + y - z \) is:

\[ \boxed{z = x + y - w} \]