Question

Se,(Anexo), determine o valor de x+y

Answer 1

Igualdade de matrizes:

Sistema:
3x-y=4   (multiplica por 3 e soma com a equação abaixo para anular "y")
x+3y=8
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10x=20
x=20/2
x=2

2+3y=8
3y=6
y=2

x+y=2+2 = 4

Answer 2

$\text{Primeiramente determinaremos os valores de 'x' e 'y'.}\\\\\begin{pmatrix}3&-1\\1&3\end{pmatrix}\cdot\begin{pmatrix}x\\y\end{pmatrix}=4\cdot\begin{pmatrix}1\\2\end{pmatrix}\\\\\\\begin{pmatrix}3x-y\\x+3y\end{pmatrix}=\begin{pmatrix}4\\8\end{pmatrix}\\\\\\\therefore\left\{\begin{matrix}3x-y&=&4\\x+3y&=&8\end{matrix}\right\\\\\\\text{Isolando 'y' da primeira e substituindo na segunda:}\\\\3x-y=4\\\\y=3x-4\\\\\\x+3y=8\\\\x+3(3x-4)=8\\\\x+9x-12=8\\\\10x-12=8\\\\10x=20\\\\x=\dfrac{20}{10}\\\\x=2\\\\\\\text{Substituindo o valor de 'x', encontramos o valor de 'y':}\\\\y=3x-4\\\\y=3(2)-4\\\\y=6-4\\\\\boxed{y=2}$




$x+y\Longrightarrow\2+2=\boxed{4}$