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Question
Find the values of (x + y) and (x – y) of the following simultaneous equations:
49x – 57y = 172
57x – 49y = 252
Sum
Solution
49x – 57y = 172 ......(i)
57x – 49y = 252 ......(ii)
Adding equations (i) and (ii),
49x – 57y = 172
+ 57x – 49y = 252
106x – 106y = 424
∴ 106(x – y) = 424
∴ x – y = `424/106`
∴ x –y = 4
Subtracting equation (ii) from equation (i),
49x – 57y = 172
– 57x + 49y = 252
– 8x – 8y = – 80
∴ –8(x – y = – 80
∴ –8(x + y) = – 80
∴ x + y = `(-80)/(-8)`
∴ x + y = 10
∴ Value of (x + y) = 10 and (x – y) = 4.
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