Question
Solve for x and y:
71x + 37y = 253,
37x + 71y = 287
71x + 37y = 253,
37x + 71y = 287
✓
Answer
The given equations are: 71x + 37y = 253 ...(1) 37x + 71y = 287 ...(2) Adding (1) and (2) 108x + 108y = 540 108(x + y) = 540 $\therefore\text{x}+\text{y}=\frac{540}{108}=5\ \dots(3)$ Subtracting (2) from (1) 34x - 34y = 253 - 287 = -34 34(x - y) = -34$\therefore\text{x}-\text{y}=- \frac{34}{34}=-1\ \dots(4)$
Adding (3) and (4) 2x = 5 - 1 = 4 ⇒ x = 2 Subtracting (4) from (3) 2y = 5 + 1 = 6 ⇒ y = 3 $\therefore$ The solution is x = 2, y = 3
Adding (3) and (4) 2x = 5 - 1 = 4 ⇒ x = 2 Subtracting (4) from (3) 2y = 5 + 1 = 6 ⇒ y = 3 $\therefore$ The solution is x = 2, y = 3
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