Question

solve this plz ( determinant and matrix)​

Answer 1

Step-by-step explanation:

$\tt \red{ \bull \: \: \: \: \: \: \: \: \: \: 2x-3y+5=0,3x+y=9 }$

$\tt \pink{ \bull \: \: \: \: \: \: \: \: \: \left(\begin{matrix}2&-3\\3&1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}-5\\9\end{matrix}\right) }$

$\tt \blue{ \bull \: \: \: \: \: \: \: \: \: \: \:\left(\begin{matrix}1&0\\0&1\end{matrix}\right)\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}2&-3\\3&1\end{matrix}\right))\left(\begin{matrix}-5\\9\end{matrix}\right) }$

$\tt \purple{ \bull \: \: \: \: \: \:\left(\begin{matrix}x\\y\end{matrix}\right)=inverse(\left(\begin{matrix}2&-3\\3&1\end{matrix}\right))\left(\begin{matrix}-5\\9\end{matrix}\right) }$

$\tt \orange{ \bull \: \: \: \: \: \: \: \:\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\dfrac{1}{2-\left(-3\times 3\right)}&-\dfrac{-3}{2-\left(-3\times 3\right)}\\-\dfrac{3}{2-\left(-3\times 3\right)}&\dfrac{2}{2-\left(-3\times 3\right)}\end{matrix}\right)\left(\begin{matrix}-5\\9\end{matrix}\right) }$

$\tt \green{ \bull \: \: \: \: \: \: \: \: \left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\dfrac{1}{11}&\dfrac{3}{11}\\-\dfrac{3}{11}&\dfrac{2}{11}\end{matrix}\right)\left(\begin{matrix}-5\\9\end{matrix}\right) }$

$\tt \red{ \bull \: \: \: \: \: \: \:\left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}\dfrac{1}{11}\left(-5\right)+\dfrac{3}{11}\times 9\\-\dfrac{3}{11}\left(-5\right)+\dfrac{2}{11}\times 9\end{matrix}\right) }$

$\tt \pink{ \bull \: \: \: \: \: \: \: \: \: \: \left(\begin{matrix}x\\y\end{matrix}\right)=\left(\begin{matrix}2\\3\end{matrix}\right) }$

$\boxed{ \boxed{ \tt \green{ \bull \: \: \: \: \: \: \: \: \: x=2,y=3 }}}$