Question

решите пж СРОЧНО!!!!!!!! очень надо

Answer 1

Ответ:

(см. объяснение)

Объяснение:

Способ 1:

$\left\{\begin{array}{c}4x-3y=9\\2x+5y=-2\end{array}\right;\\\\\left(\begin{array}{cc}4&-3\\2&5\end{array}\right)\left[\begin{array}{c}x\\y\end{array}\right]=\left(\begin{array}{c}9\\-2\end{array}\right)\\\\\left[\begin{array}{c}x\\y\end{array}\right]=\left(\begin{array}{cc}4&-3\\2&5\end{array}\right)^{-1}\left(\begin{array}{c}9\\-2\end{array}\right)=\dfrac{1}{26}\left(\begin{array}{cc}5&3\\-2&4\end{array}\right)\left(\begin{array}{c}9\\-2\end{array}\right)=\left(\begin{array}{c}3/2\\-1\end{array}\right)$

$\left\{\begin{array}{c}x=3/2\\y=-1\end{array}\right;$

Способ 2:

$\left\{\begin{array}{c}4x-3y=9\\2x+5y=-2\end{array}\right;\\\\\Delta=\left|\begin{array}{cc}4&-3\\2&5\end{array}\right|=26\\\Delta_1=\left|\begin{array}{cc}9&-3\\-2&5\end{array}\right|=39\\\Delta_2=\left|\begin{array}{cc}4&9\\2&-2\end{array}\right|=-26\\x=\dfrac{\Delta_1}{\Delta}=3/2\\\\y=\dfrac{\Delta_2}{\Delta}=-1$

$\left\{\begin{array}{c}x=3/2\\y=-1\end{array}\right;$

Способ 3:

$\left\{\begin{array}{c}4x-3y=9\\2x+5y=-2\end{array}\right;\\\\\left(\begin{array}{cc}4&-3\\2&5\end{array}\left|\begin{array}{c}9\\-2\end{array}\right\right)\sim\left(\begin{array}{cc}2&5\\0&-1\end{array}\left|\begin{array}{c}-2\\1\end{array}\right\right)\sim\left(\begin{array}{cc}2&0\\0&-1\end{array}\left|\begin{array}{c}3\\1\end{array}\right\right)$

$x,\;y$ - базисные.

$\left\{\begin{array}{c}2x=3\\-y=1\end{array}\right,\;\left\{\begin{array}{c}x=3/2\\y=-1\end{array}\right;$

Графический и вариации школьных аналитических способов опускаю.

Система уравнений решена!