[tex]\displaystyle\begin{cases}p+q+r=15\\ p-q-r=-3\\ 2p+q+3r=29\end{cases}\\\\\\\sf\frac{r}{p}+q=....[/tex]
(A) 5 ⅔ (B) 6 ⁴/₅ (C) 7 ¼ (D) 2 ³/₅ (E) 3 ¾
Jawaban:
A
Penjelasan dengan langkah-langkah:
p + q + r = 15
p - q - r = - 3 +
2p = 12
p = 12/2
p = 6
2p + q + 3r = 29
q + 3r = 29 - 2p
q + 3r = 29 - 2(6)
q + 3r = 17
q = 17 - 3r
p + q + r = 15
6 + 17 - 3r + r = 15
23 - 2r = 15
2r = 23 - 15
r = 8/2
r = 4
q = 17 - 3(4)
q = 17 - 12
q = 5
r/p + q = 4/6 + 5
r/p + q = 5⅔
Penyelesaian:
[tex]\begin{cases}p+q+r=15\\ p-q-r=-3\\ 2p+q+3r=29\end{cases}[/tex]
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r/p +q=?
Dari persamaan 2 didapat nilai r:
r=p-q+3
q=p-r+3
Maka:
Substitusikan pada kedua persamaan 1
p+q+r=15
p+q+p-q+3=15
2p+3=15
2p=12
p=6
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Substitusikan pada persamaan 3
2p+q+3r=29
2(6)+p-r+3+3r=29
12+6+2r+3=29
2r+12=20
2r=8
r=4
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q=p-r+3
q=6-4+3
q=5
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r/p+q
=4/6 +5
=5⅔(A.)
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[tex] \boxed{ \colorbox{black}{ \sf{ \color{lightgreen}{ answered\:by\:Duone}}}} [/tex]
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