Find 𝑥, 𝑦, 𝑧 such that (𝑥-𝑦, 𝑥+𝑦, 𝑧-1)=(4,2,3)

From the given equation, we have three separate equations:

1. 𝑥 - 𝑦 = 4
2. 𝑥 + 𝑦 = 2
3. 𝑧 - 1 = 3

Let's solve these equations one by one:

1. From the first equation, we can express 𝑦 in terms of 𝑥: 𝑦 = 𝑥 - 4
2. Substitute 𝑦 = 𝑥 - 4 into the second equation: 𝑥 + (𝑥 - 4) = 2, which simplifies to 2𝑥 - 4 = 2. Solving for 𝑥 gives 𝑥 = 3.
3. Substitute 𝑥 = 3 into 𝑦 = 𝑥 - 4 to find 𝑦 = 3 - 4 = -1.
4. From the third equation, we can solve for 𝑧: 𝑧 = 3 + 1 = 4.

So, the solution to the system of equations is 𝑥 = 3, 𝑦 = -1, 𝑧 = 4.