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31 votes
31 votes
Find x and y in

(i) 23x- 29y= 98 and 29x -23y =110
(ii) 99x +101y =499 and 101x +99y =501

User Arfa
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1 Answer

20 votes
20 votes

Answer:

23 x-29y=98.......(1)

29 x-23y=110.......(2)

adding (1) and (2)we get

52 x-52y=208

52(x+y)=208

x-y=4...(3)[we get four by dividing 208 with 52]

subtract (2) from (1) we get

-6 x-6y=-12

x-y=2.....(4)

adding (3) and (4) we get

2x=6

therefore x=3

now from (4) we get

x-y=2 [we substitute xfor 3]

3-y=2

y=2-3

y=-1( that is the answer for your first question)

Explanation:

99x+101y=499.....(1)

101x+99y=501.....(2)

add (1) and (2)

(99+101)x+(101+99)=(499+501)

200x+200y=1000

200(x+ y)=1000

x+y=5.....(3)

subtract (2)from(1) we get

2x-2y=2

2(x-y)=2

x+y=1.......(4)

x+y=5

x-y=1(add them together)

2x=6

x=3

substitute x equal to 3 in equation (3)

x+y=5

3+y=5

y=2

y equal to 2 and x equal to 3

hope is not too late

User DannyA
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