[tex]\frac { \frac { 2 } { 3 } x + \frac { 1 } { 6 } y - \frac { 3 } { 2 } z + 2 } { \frac { 5 } { 2.... Question from @Osaze12345

May 2022 1 1 Report

[tex]\frac { \frac { 2 } { 3 } x + \frac { 1 } { 6 } y - \frac { 3 } { 2 } z + 2 } { \frac { 5 } { 2 } z + \frac { 2 } { 7 } x - 2 \frac { 1 } { 3 } y - 5 } = 2[/tex]
sederhanakan plis

henriyulianto

Bentuk sederhana: $\bf 4x+203y-273z=-504$

Pembahasan

$\begin{aligned}&\frac{\left(\dfrac{2}{3}x+\dfrac{1}{6}y-\dfrac{3}{2}z+2\right)}{\left(\dfrac{5}{2}z+\dfrac{2}{7}x-2\dfrac{1}{3}y-5\right)}=2\\&{\rightsquigarrow\ \ }\frac{\left(\dfrac{2}{3}x+\dfrac{1}{6}y-\dfrac{3}{2}z+2\right)}{\left(\dfrac{5}{2}z+\dfrac{2}{7}x-\dfrac{7}{3}y-5\right)}=2\\\end{aligned}$

Pada pembilang, penyebut pecahan-pecahan koefisien variabel adalah 3, 6, dan 2. KPK dari 3, 6, dan 2 adalah 6. Maka, jadikan pecahan-pecahan berpenyebut 6.

$\begin{aligned}&{\rightsquigarrow\ \ }\frac{\left(\dfrac{4}{6}x+\dfrac{1}{6}y-\dfrac{9}{6}z+\dfrac{12}{6}\right)}{\left(\dfrac{5}{2}z+\dfrac{2}{7}x-\dfrac{7}{3}y-5\right)}=2\\\end{aligned}$

Pada penyebut, penyebut pecahan-pecahan koefisien variabel adalah 2, 7, dan 3. KPK dari 2, 7, dan 3 adalah 42. Maka, jadikan pecahan-pecahan berpenyebut 42.

$\begin{aligned}&{\rightsquigarrow\ \ }\frac{\left(\dfrac{4}{6}x+\dfrac{1}{6}y-\dfrac{9}{6}z+\dfrac{12}{6}\right)}{\left(\dfrac{105}{42}z+\dfrac{12}{42}x-\dfrac{98}{42}y-\dfrac{210}{42}\right)}=2\\\end{aligned}$

Lalu, sederhanakan.

$\begin{aligned}&{\rightsquigarrow\ \ }\frac{\left(\dfrac{4x+y-9z+12}{6}\right)}{\left(\dfrac{105z+12x-98y-210}{42}\right)}=2\\&{\rightsquigarrow\ \ }\frac{\left(\dfrac{4x+y-9z+12}{\cancel{6}}\right)}{\left(\dfrac{105z+12x-98y-210}{42}\right)}\times\frac{\cancel{6}}{6}=2\\&{\rightsquigarrow\ \ }\frac{4x+y-9z+12}{\left(\dfrac{105z+12x-98y-210}{7}\right)}=2\\&{\rightsquigarrow\ \ }\frac{7(4x+y-9z+12)}{105z+12x-98y-210}=2\end{aligned}$
$\begin{aligned}&{\rightsquigarrow\ \ }\frac{28x+7y-63z+84}{105z+12x-98y-210}=2\\&{\rightsquigarrow\ \ }28x+7y-63z+84=2(105z+12x-98y-210)\\&{\rightsquigarrow\ \ }28x+7y-63z+84=210z+24x-196y-420\\&{\rightsquigarrow\ \ }28x-24x+7y+196y-63z-210z=-420-84\\&{\therefore\ \ }\boxed{\ \bf 4x+203y-273z=-504\ }\\\end{aligned}$