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Question
Solve the following system of equations:
101x + 102y = 304
102x + 101y = 305
Sum
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Solution
Given: 101x + 102y = 304, 102x + 101y = 305.
Step-wise calculation:
1. Subtract the first equation from the second:
(102x – 101x) + (101y – 102y) = 305 – 304
⇒ x – y = 1
⇒ x = y + 1
2. Substitute x = y + 1 into 101x + 102y = 304:
101(y + 1) + 102y = 304
⇒ 101y + 101 + 102y = 304
⇒ 203y + 101 = 304
⇒ 203y = 203
⇒ y = 1
3. Then x = y + 1 = 2.
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