Question:
If \( (x,y,z) \) is the solution of the equations
\[
x - y - 2z = 3,
2x + y + 4z = 5,
4x - y - 2z = 11,
\]
then the value of \( y \) equals
If \( (x,y,z) \) is the solution of the equations
\[
x - y - 2z = 3,
2x + y + 4z = 5,
4x - y - 2z = 11,
\]
then the value of \( y \) equals
Show Hint
Eliminate one variable at a time to simplify multi-variable systems efficiently.
Updated On: Apr 30, 2026
- \( 0 \)
- \( -\frac{1}{2} \)
- \( -\frac{1}{3} \)
- \( -\frac{1}{4} \)
- \( -1 \)
Show Solution
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The Correct Option is C
Solution and Explanation
Concept:
Solve simultaneous linear equations using elimination.
Step 1: Write equations. \[ (1)\ x - y - 2z = 3 \] \[ (2)\ 2x + y + 4z = 5 \] \[ (3)\ 4x - y - 2z = 11 \]
Step 2: Eliminate \(y\). Add (1) and (2): \[ 3x + 2z = 8 \cdots (4) \] Subtract (1) from (3): \[ 3x = 8 \Rightarrow x = \frac{8}{3} \]
Step 3: Find \(z\). From (4): \[ 3\left(\frac{8}{3}\right) + 2z = 8 \Rightarrow 8 + 2z = 8 \Rightarrow z = 0 \]
Step 4: Find \(y\). From (1): \[ \frac{8}{3} - y = 3 \Rightarrow y = \frac{8}{3} - 3 = -\frac{1}{3} \]
Step 1: Write equations. \[ (1)\ x - y - 2z = 3 \] \[ (2)\ 2x + y + 4z = 5 \] \[ (3)\ 4x - y - 2z = 11 \]
Step 2: Eliminate \(y\). Add (1) and (2): \[ 3x + 2z = 8 \cdots (4) \] Subtract (1) from (3): \[ 3x = 8 \Rightarrow x = \frac{8}{3} \]
Step 3: Find \(z\). From (4): \[ 3\left(\frac{8}{3}\right) + 2z = 8 \Rightarrow 8 + 2z = 8 \Rightarrow z = 0 \]
Step 4: Find \(y\). From (1): \[ \frac{8}{3} - y = 3 \Rightarrow y = \frac{8}{3} - 3 = -\frac{1}{3} \]
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