Question

SPLDV
5x+3y=9
3x-2y=11

Hanya sebuah kuis ​

Answer 1

Verified answer

Sistem Persamaan Linear Dua Variabel

[Metode Invers Matriks]

..

[tex]\begin{cases} 5x+3y = 9 \\ 3x - 2y = 11 \end{cases}[/tex]

Bentuk Matriks

[tex]\begin{bmatrix} 5&3\\3&-2 \end{bmatrix}\begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 9 \\ 11 \end{bmatrix}[/tex]

Himpunan Penyelesaian

[tex]\begin{aligned} \begin{bmatrix} x \\ y \end{bmatrix} &= \begin{bmatrix} 5&3\\3&-2 \end{bmatrix}^{-1} \begin{bmatrix} 9\\11 \end{bmatrix} \\\begin{bmatrix} x \\ y \end{bmatrix} &= \left(\frac{1}{5 \times (-2) - 3 \times 3} \right) \begin{bmatrix} -2&-3\\-3&5 \end{bmatrix} \begin{bmatrix} 9 \\ 11 \end{bmatrix} \\\begin{bmatrix} x \\ y \end{bmatrix} &= \left(\frac{1}{-10 - 9} \right) \begin{bmatrix} (-2) \times 9 + (-3) \times 11 \\(-3) \times 9 + 5 \times 11 \end{bmatrix} \\ \begin{bmatrix} x \\ y \end{bmatrix} &= \left(-\frac{1}{19} \right) \begin{bmatrix} -51 \\28\end{bmatrix} \\\begin{bmatrix} x \\ y \end{bmatrix} &= \begin{bmatrix} \frac{51}{19} \\ -\frac{28}{19} \end{bmatrix} \end{aligned}[/tex]

[tex]\displaystyle \rm{HP} = \left\{ \frac{51}{19}, -\frac{28}{19} \right\}[/tex]

[tex]\boxed{\colorbox{ccddff}{Answered by Danial Alf'at | 29 - 05 - 2023}}[/tex]