If 2x y + 3z = 2, what is the value of y?

NOTE: Some students will conclude that neither statement alone is sufficient because, in order to solve a linear system with 3 variables, we need at least 3 different equations.
While it's true that we need at least 3 different equations to find the individual value of each of the 3 variables, it's still possible to solve for ONE variable given fewer than 3 equations.
For example, if b + c = 10 and b + c + d = 17, then I can be certain that d = 7 (even though there's no way to determine the values of b and c)

With that in mind, let's move on to the question:

Given: 2x – y + 3z = 2

Target question: What is the value of y?

Statement 1: -4x + 2y - 5 = 3z
This means we now have the following linear system:
-4x + 2y - 5 = 3z
2x – y + 3z = 2

Let's see if we can eliminate the variables x and z to leave only y's (aka solving for y)

Let's multiply both sides of the bottom equation by 2 (so that the coefficients in both equations are similar), and rearrange the terms in the top equation so that they're similar to those in the bottom equation.
When we do this, we get:
-4x + 2y - 3z = 5
4x – 2y + 6z = 4

Add the two equations to get: 3z = 9, which means z = 3.

Now that we know z = 3, we can plug this value into our two equations to get:
-4x + 2y - 3(3) = 5
4x – 2y + 6(3) = 4

Simplify and rearrange:
-4x + 2y = 14
4x – 2y = -14
At this point, we can see that our two equations are equivalent, which means there's no way to solve for the values of x and y.

Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: -2x - 3 = 3z - 2y
We now have the following linear system:
-2x - 3 = 3z - 2y
2x – y + 3z = 2

Rearrange the terms in the top equation so that they're similar to the terms in the bottom equation:
-2x + 2y - 3z = 3
2x – y + 3z = 2

Add the two equations to get: y = 5
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B