Step-by-Step Solution
Key Concept: For symmetric linear equations $ax + by = c$ and $bx + ay = d$, add both equations to get $(x + y)$ and subtract both to get $(x - y)$.
Add both equations: $(152 - 378)x + (-378 + 152)y = -74 - 604 \Rightarrow -226x - 226y = -678 \Rightarrow x + y = 3$ -- (eq 1). [1.0 Mark]
Subtract first equation from second: $(-378 - 152)x + (152 + 378)y = -604 - (-74) \Rightarrow -530x + 530y = -530 \Rightarrow -x + y = -1$ -- (eq 2). [1.0 Mark]
Add eq 1 and eq 2: $2y = 2 \Rightarrow y = 1$.
Substitute $y = 1$ into eq 1: $x + 1 = 3 \Rightarrow x = 2$. Solution: $x = 2, y = 1$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Adding equations to get $x + y = 3$: 1.0 Mark
Subtracting equations to get $-x + y = -1$: 1.0 Mark
Solving for $x = 2, y = 1$: 1.0 Mark
Correct Answer: