Finding x, y, z
Question:
Solve: \[ [x,\; y+2,\; z-3] + [y,\; 4,\; 5] = [4,\; 9,\; 12] \]
Solve: \[ [x,\; y+2,\; z-3] + [y,\; 4,\; 5] = [4,\; 9,\; 12] \]
Solution:
Step 1: Add corresponding elements
\[ [x+y,\; y+6,\; z+2] = [4,\; 9,\; 12] \]Step 2: Compare corresponding elements
\[ x + y = 4 \quad …(1) \] \[ y + 6 = 9 \Rightarrow y = 3 \quad …(2) \] \[ z + 2 = 12 \Rightarrow z = 10 \quad …(3) \]Step 3: Substitute value of \(y\)
\[ x + 3 = 4 \Rightarrow x = 1 \]Final Answer:
\[ x = 1,\quad y = 3,\quad z = 10 \]