Check whether the pair of equations $x + 3y = 6$ and $2x - 3y = 12$ is consistent. If so, solve them algebraically.
Step-by-Step Solution
Key Concept: $\\dfrac{a_1}{a_2} = \\dfrac{1}{2}$, $\\dfrac{b_1}{b_2} = \\dfrac{3}{-3} = -1$. Since $1/2 <br>eq -1$, consistent with unique solution.
$a_1/a_2 = 1/2
eq b_1/b_2 = -1 \Rightarrow$ Consistent (unique solution). [0.5 Mark]
Add equations: $(x + 3y) + (2x - 3y) = 6 + 12 \Rightarrow 3x = 18 \Rightarrow x = 6$. [1.0 Mark]
$6 + 3y = 6 \Rightarrow 3y = 0 \Rightarrow y = 0$. Solution: $x = 6, y = 0$. [0.5 Mark]
---
🎯 Official CBSE Marking Scheme:
Checking consistency condition: 0.5 Mark
Solving $x = 6$: 1.0 Mark
Solving $y = 0$: 0.5 Mark
Correct Answer: