Find the value of Y, if X - 2Y + 2Z = 16, X - Y + Z = 9 and 2X - 3Y - Z = 9.
-3
We have the following system of equations: 1) X - 2Y + 2Z = 16 2) X - Y + Z = 9 3) 2X - 3Y - Z = 9 Subtracting equation (2) from equation (1), we get -Y + Z = 7. Adding equation (2) and equation (3), we get 3X - 4Y = 18. From -Y + Z = 7, we get Z = 7 + Y. Substitute Z = 7 + Y into equation (2): X - Y + 7 + Y = 9, which simplifies to X = 2. Substitute X = 2 into 3X - 4Y = 18: 3(2) - 4Y = 18, which simplifies to 6 - 4Y = 18. Solving for Y, we get -4Y = 12, so Y = -3.
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