For-matris-solution-2x-3y-8-x-5y-9-

Question Number 150807 by mathdanisur last updated on 15/Aug/21

For matris solution :

{\begin{cases} 2 x - 3 y = 8 \\ x + 5 y = - 9 \end{cases}

Answered by maged last updated on 15/Aug/21

Δ =∣ \underset{⏟}{}

Answered by amin96 last updated on 15/Aug/21

C r a m e r m e t h o d

Δ = | \begin{matrix} 2 & - 3 \\ 1 & 5 \end{matrix} | = 10 + 3 = 13

Δ_{x} = | \begin{matrix} 8 & - 3 \\ - 9 & 5 \end{matrix} | = 40 - 27 = 13

Δ_{y} = | \begin{matrix} 2 & 8 \\ 1 & - 9 \end{matrix} | = - 18 - 8 = - 26

x = \frac{Δ_{x}}{Δ} = \frac{13}{13} = 1

y = \frac{Δ_{y}}{Δ} = \frac{- 26}{13} = - 2 (1; - 2)

Commented by mathdanisur last updated on 15/Aug/21

cool thanks Ser

Commented by puissant last updated on 15/Aug/21

n i c e s i r C r a m e r m e t h o d . .

Answered by amin96 last updated on 15/Aug/21

G a u s m e t h o d

{(\begin{matrix} 1 & 5 & - 9 \\ 2 & - 3 & 8 \end{matrix})}^{(1) \cdot 2 - (2)} = (\begin{matrix} 1 & 5 & - 9 \\ 0 & 13 & - 26 \end{matrix}) \Rightarrow

\Rightarrow {\begin{cases} x + 5 y = - 9 \\ 13 y = - 26 \end{cases} \Rightarrow {\begin{cases} x = 1 \\ y = - 2 \end{cases} (1; - 2)

Commented by mathdanisur last updated on 15/Aug/21

cool thankyou Ser

Answered by maged last updated on 15/Aug/21

Answered by physicstutes last updated on 16/Aug/21

\boldsymbol Another \boldsymbol matrix \boldsymbol method \boldsymbol approach .

{\begin{cases} 2 x - 3 y = 8 \dots \dots (i) \\ x + 5 y = - 9 \dots \dots (i i) \end{cases}

\Rightarrow (\begin{matrix} 2 & - 3 \\ 1 & 5 \end{matrix}) (\begin{matrix} x \\ y \end{matrix}) = (\begin{matrix} 8 \\ - 9 \end{matrix})

\Rightarrow (\begin{matrix} x \\ y \end{matrix}) = {(\begin{matrix} 2 & - 3 \\ 1 & 5 \end{matrix})}^{- 1} (\begin{matrix} 8 \\ - 9 \end{matrix}) = \frac{1}{13} (\begin{matrix} 5 & 3 \\ - 1 & 2 \end{matrix}) (\begin{matrix} 8 \\ - 9 \end{matrix}) = (\begin{matrix} 1 \\ - 2 \end{matrix})