Question

Tentukan himpunan penyelesaian dari sistem persaman linear dua variabel berikut!
[tex]12x + 13y = 80 \\ 14x - 15y = 90[/tex]
​

Answer 1

Jawaban:

[tex](x. \: y) = ( \frac{1185}{181} . \: \frac{20}{181} )[/tex]

Penjelasan dengan langkah-langkah:

[tex]12x + 13y = 80 \: ( \times 15)[/tex]

[tex]14x - 15y = 90 \: ( \times 13)[/tex]

..

[tex]180x + 195y = 1200[/tex]

[tex]182x - 195y = 1170[/tex]

_________________________+

[tex] 362x = 2370[/tex]

[tex]x = \frac{2370}{362} [/tex]

[tex]x = \frac{1185}{181} [/tex]

..

[tex]12( \frac{1185}{181} ) + 13y = 80[/tex]

[tex] \frac{14220}{181} + 13y = 80[/tex]

[tex]13y = \frac{14480}{181} - \frac{14220 }{181} [/tex]

[tex]13y = \frac{260}{181} [/tex]

[tex]y = \frac{20}{181} [/tex]

[tex]\boxed{\colorbox{ccddff}{Answered by Danial Alf'at}}[/tex]

Answer 2

Verified answer

Penjelasan dengan langkah-langkah:

Variabel

12x + 13y = 80 ...... ( × 14)

14x - 15y = 90 ...... ( × 12)

.

.

168x + 182y = 1120

168x - 180y = 1080

----------------------------- (-)

362y = 40

y = 40/362

y = 20/181

12x + 13y = 80

12x + 13(20/181) = 80

12x + 260/181 = 80

12x = 80 - 260/181

12x = 14220/181

x = 14220/181 ÷ 12

x = 14220/181 × 1/12

x = 1185/181

Maka

{x,y} = { 1185/181 , 20/181 }