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Question
Solve for x and y:
23x + 24y = 23
24x + 23y = 24
Sum
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Solution
Given: 23x + 24y = 23, 24x + 23y = 24
Step-wise calculation:
1. Add the two equations:
(23x + 24y) + (24x + 23y) = 23 + 24
⇒ 47x + 47y = 47
⇒ x + y = 1
2. Subtract the first equation from the second:
(24x + 23y) – (23x + 24y) = 24 – 23
⇒ x – y = 1
3. Solve the pair x + y = 1 and x – y = 1:
Add them ⇒ 2x = 2 ⇒ x = 1.
Substitute x = 1 into x + y = 1 ⇒ y = 0.
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