حل تشریحی سوال شماره 24 ریاضی (مشهد)

$\frac{1}{2}\left[\begin{array}{c}2x-6\\ 2y-6x\end{array}\right]-2\left[(2x-8)\vec{i}+(2y+2)\vec{j}\right]=(-5)(\vec{i}+\vec{j})$

$\frac{1}{2}\left[\begin{array}{c}2x-6\\ 2y-6x\end{array}\right]-2\left[\begin{array}{c}2x-8\\ 2y+2\end{array}\right]=-5\left[\begin{array}{c}1\\ 1\end{array}\right]$

$\left[\begin{array}{c}x-3\\ y-3x\end{array}\right]-\left[\begin{array}{c}4x-16\\ 4y+4\end{array}\right]=\left[\begin{array}{c}-5\\ -5\end{array}\right]$

$\{\begin{array}{c}x-3-4x+16=-5\Rightarrow -3x=-18\Rightarrow x=6\\ y\underset{-18}{\cancel{-3(6)}}-4y-4=-5\Rightarrow -3y=17\Rightarrow y=\frac{-17}{3}\end{array}$