Which answer choice shows 2x-y=z correctly solved for y?

A: y=2x+z B: y=2x-z C:y=-2x+z D: y=-2x-z

Here's how I did it:

2x-y=z
-y=2x+z
y=-2x-z

Am I right? I have a feeling I'm not, so I would like some confirmation one way or the other.

2 x - y = z Add y to both sides

2 x - y + y = z + y

2 x = z + y Subtract z to both sides

2 x - z = z + y - z

2 x - z = y

y = 2 x - z

Yes, you are correct! Let's go through the steps to solve 2x-y=z for y.

Step 1: Start with the equation 2x-y=z.
Step 2: Your instinct to add y to both sides is correct. By adding y to both sides, we get -y+y=2x+z+y, which simplifies to 0=2x+z+y.
Step 3: To solve for y, we need to isolate it on one side of the equation. By subtracting 2x and z from both sides, 0-2x-z=2x+z+y-2x-z. This simplifies to -2x-z=y.
Step 4: Now, let's rewrite the equation with y on the left side. Therefore, y=-2x-z.

Therefore, the correct answer is D: y=-2x-z.