d. {1/2 , 1/5 }

Diposting pada

Pertanyaan :


1. himpunan penyelesaian sistem persamaan 2/x – 5/y = 21 dan 1/x + 2/y= 8 adalah ……………………..


a. {-1/2 , -1/5 }
b. {1/2 , -1/5 }
c. {-1 /2, 1/5 }
d. {1/2 , 1/5 }

Jawaban :

2/x – 5/y = 21
(2y – 5x)/xy = 21
2y – 5x = 21xy
2y = 21xy + 5x
y = (21xy + 5x)/2

1/x + 2/y = 8
(y + 2x)/xy = 8
y + 2x = 8xy
(21xy + 5x)/2 + 2x = 8xy
(21xy + 5x + 4x)/2 = 8xy
21xy + 9x = 2(8xy)
21xy + 9x = 16xy
21xy – 16xy = -9x
5xy = -9x
5y = -9
y = -9/5

y + 2x = 8xy
-9/5 + 2x = 8(-9/5)x
-9/5 + 2x = -72/5x
-9/5 = -72/5x – 2x
-9/5 = -72/5x – 10/5x
-9/5 = -82/5x
-9 = -82x
x = -9/-82
x = 9/82

HP = {9/82 , -9/5)

tidak ada pada opsi.

pembuktian :

2/(9/82) – 5/(-9/5) = 21
164/9 + 25/9 = 21
189/9 = 21
21 = 21
QED

1/(9/82) + 2/(-9/5) = 8
82/9 – 10/9 = 8
72/9 = 8
8 = 8
QED

solusi tidak terdapat pada opsi.

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