Question

Encontrar o Valor do Y neste sistema

x-5z=2
3x-y-5z=3
4x-4y-3z=-4

Queria os calculos tb

Answer 1

I) x - 5z = 2 => x = 2 + 5z
II) 3.(2 + 5z) - y - 5z =3 => 6 + 15z - y - 5z = 3 =>  -y + 10z = 3 - 6 = -y + 10z = -3 => -y = -3 - 10z => y = 3 + 10z
III) 4.(2 + 5z) - 4.(3 + 10z) - 3z = 4 => 8 + 20z - 12 + 40z - 3z = 4 => 57z = 4 + 12 - 8 => 57z = 8 => z = 8/57 = 1/7

II) y = 3 + 10z => y = 3 + 10.1/7 => y = 3 + 10/7 => y = 21/7 + 10/7 => y = 31/7

I) x = 2 + 5z => x = 2 + 5.1/7 => x = 2 + 5/7 => x = 14/7 + 5/7 => x = 19/7

Answer 2

$x = 5z + 2 ;$ $3x -y - 5z=3; 3 (2 + 5z) - y - 5z = 3--\ \textgreater \ 6 + 15z - 5z - 3 =y ;$ $y= 10z + 3 ;$ $4x - 4y - 3z = -4; 4.(5z + 2) - 4. ( 10z + 3 ) - 3z = - 4;$ $20z + 8 - 40z - 12 - 3z = - 4--\ \textgreater \ -23z = -4 + 4; -23z=0; z = 0$ $y= 10z + 3 = 10.0 + 3--\ \textgreater \ y = 3$