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प्रश्न
Solve the following system of equations:
21x + 47y = 110
47x + 21y = 162
योग
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उत्तर
Given: 21x + 47y = 110; 47x + 21y = 162.
Step-wise calculation:
1. Add the two equations:
(21x + 47x) + (47y + 21y) = 110 + 162
68x + 68y = 272
⇒ x + y = 4
2. Subtract the first equation from the second:
(47x – 21x) + (21y – 47y) = 162 – 110
26x – 26y = 52
⇒ x – y = 2
3. Solve the two simpler equations:
Add x + y = 4 and x – y = 2
⇒ 2x = 6
⇒ x = 3
Substitute x = 3 into x + y = 4
⇒ y = 1
The solution is x = 3, y = 1 (ordered pair (3, 1)).
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