NO NGASAL ASAL!!! Nilai y + [tex] \sqrt{x^2 - 2xz+z^2} [/tex] dari sistem persamaan : [tex] y + \dfrac{2}{x+z} = 4 \\\\ 5y + \dfrac{18}{2x+y+z} = 18 \\\\ \dfrac

[tex] y + \frac{2}{x + z } = 4 \\
\frac{2}{x + z } = 4 - y \ ... (i) [/tex]

[tex] 5y + \frac{18}{2x+y+z} = 18 \\
\frac{18}{2x+y+z} = 18 - 5y \\
\frac{3 \cdot 6}{2x + y + z} = 18 - 5y \\
\frac{6}{2x + y + z} = 6 - \frac53y \ ... (ii) [/tex]

[tex] Didapat \ : \\
\frac{8}{x + z} - \frac{6}{2x + y + z} = 3 \\
4 (\frac{2}{x + z}) - \frac{6}{2x + y + z} = 3 \\
Subtitusi \ persamaan \ (i) \ dan \ (ii) \ : \\
4(4 - y) - (6 - \frac53y) = 3 \\
16 - 4y - 6 + \frac53y = 3 \\
- \frac73y = - 7 \\
y = 3 \ ... (iii) [/tex]

Subtitusikan persamaan (iii) ke (i)
[tex] \frac{2}{x + z } = 4 - y \\
\frac{2}{x + z } = 4 - 3 \\
\frac{2}{x + z } = 1 [/tex]
x + z = 2 ... (iv)

Subtitusikan persamaan (iii) ke (ii)
[tex] \frac{6}{2x + y + z} = 6 - \frac53y \\
\frac{6}{2x + 3 + z} = 6 - \frac53 \times 3 \\
\frac{6}{2x + 3 + z} = 1 [/tex]
6 = 2x + 3 + z
2x + z = 3 ... (v)

Eliminasi persamaan (iv) dan (v)

x + z = 2
2x + z = 3
––––––– (–)
-x = -1
x = 1

Subtitusikan x = 1 ke persamaan (iv)
x + z = 2
1 + z = 2
z = 1

Didapat x = 1 , y = 3 , z = 1

Maka :
[tex] y + \sqrt{x^2 - 2xz + z^2} \\
= y + \sqrt{ (x - z)^2 } [/tex]
= y + |x - z|
= 3 + |1 - 1|
= 3

koreksi jika ada kesalahan