Question

Tentukan himpunan penyelesaian dari sistem persamaan linier berikut dengan eliminasi. ​

Answer 1

Jawab:

HP = {4, 8}

Penjelasan dengan langkah-langkah:

[tex]\displaystyle \left\{\begin{matrix}\frac{y+2}{5}+\frac{x-1}{3}=3\\ \frac{y-2}{6}-\frac{3x+2}{7}=-1\end{matrix}\right.\\\left\{\begin{matrix}\frac{3(y+2)+5(x-1)}{15}=3\\ \frac{7(y-2)-6(3x+2)}{42}=-1\end{matrix}\right.\\\left\{\begin{matrix}5x+3y=44\\ -18x+7y=-16\end{matrix}\right.[/tex]

Eliminasi x

[tex]\displaystyle \left.\begin{matrix}5x+3y=44\\ -18x+7y=-16\end{matrix}\right|\left.\begin{matrix}\times 18\\ \times 5\end{matrix}\right|\begin{matrix}90x+54y=792\\ -90x+35y=-80\end{matrix}[/tex]

90x + 54y = 792

-90x + 35y = -80

_____________

89y = 712 → y = 8

Eliminasi y

[tex]\displaystyle \left.\begin{matrix}5x+3y=44\\ -18x+7y=-16\end{matrix}\right|\left.\begin{matrix}\times 7\\ \times 3\end{matrix}\right|\begin{matrix}35x+21y=308\\ -54x+21y=-48\end{matrix}[/tex]

35x + 21y = 308

-54x + 21y = -48

____________

89x = 356 → x = 4