Question

me ajude a como resolver esse sistema para achar X e Y
3X+Y=A-B
-3X-2Y=B-2A

Answer 1

$\left \{ {2X+Y{=A-B} \atop {-3X-2Y=B-2A}} \right.$, somando-se as duas:
$-X-Y=-A, X+Y=A$
Podemos escrever a primeira equação como:
$X+X+Y=A-B$, porém $X+Y=A$, logo:
$X=-B$, sendo assim:
$X= \left[\begin{array}{ccc}2&-6\\1&-7\end{array}\right]$, aplicando-se os valores de X e de A na equação $X+Y=A$, temos:
$\left[\begin{array}{ccc}2&-6\\1&-7\\\end{array}\right] + \left[\begin{array}{ccc}a_{11}&a_{12}\\a_{21}&a_{22}\\\end{array}\right] = \left[\begin{array}{ccc}2&-3\\0&5\\\end{array}\right]$, logo:
$\left[\begin{array}{ccc}a_{11}+2&a_{12}-6\\a_{21}+1&a_{22}-7\\\end{array}\right] = \left[\begin{array}{ccc}2&-3\\0&5\\\end{array}\right]$, sendo assim:
$a_{11}+2=2,a_{11}=0, a_{12}-6=-3,a_{12}=3$
$a_{21} +1=0,a_{21}=-1,a_{22}-7=5,a_{22}=12$, logo:
$X= \left[\begin{array}{ccc}2&-3\\0&5\\\end{array}\right],Y= \left[\begin{array}{ccc}0&3\\-1&12\\\end{array}\right]$