HOTS Zone : Sistem Persamaan Aljabar

Table of Contents

No. 1

x, y dan z adalah tiga bilangan real dari sistem persamaan
(x + y)(x + y + z) = 132
(y + z)(x + y + z) = 84
(z + x)(x + y + z) = 72
Nilai dari x + 2y − 3z = ....

1. 16
2. 18
3. 20
4. 22
5. 24

PEMBAHASAN

$\begin{array}{rl}(x+y)(x+y+z)& =132\\ (y+z)(x+y+z)& =84\\ (z+x)(x+y+z)& =72& +\\ -------------------------& ---------& \\ 2(x+y+z)(x+y+z)& =288\\ (x+y+z{)}^2& =144\\ x+y+z& =12\end{array}$

$\begin{array}{rl}(x+y)(x+y+z)& =132\\ (x+y)(12)& =132\\ x+y& =11\\ x+y+z-z& =11\\ 12-z& =11\\ z& =1\end{array}$

$\begin{array}{rl}(y+z)(x+y+z)& =84\\ (y+1)(12)& =84\\ y& =6\end{array}$

$\begin{array}{rl}x+y+z& =12\\ x+6+1& =12\\ x& =5\end{array}$

$\begin{array}{rl}x+2y-3z& =5+2(6)-3(1)\\ & =5+12-3\\ & =\boxed{{\displaystyle \boxed{{\displaystyle 14}}}}\end{array}$