Determine o valor de a , de modo que a terna (a, -2, 1-2a) seja solução da equação linear 5×+y-2z=13 .
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![(a,-2,1-2a)\\\\\\\
5x+y-2z=13](https://tex.z-dn.net/?f=%28a%2C-2%2C1-2a%29%5C%5C%5C%5C%5C%5C%5C%0A5x%2By-2z%3D13 "(a,-2,1-2a)\\\\\\\
5x+y-2z=13")
![x=a\\\\\
y=-2\\\\\
z=1-2a\\\\\\\\
Substituindo~~na~~equac\~ao!\\\\\\\
5(a)+(-2)-2(1-2a)=13\\\\\\\
5a-2-2+4a=13\\\\\\\
5a-4+4a=13\\\\\\
5a+4a=13+4\\\\\\
9a=17\\\\\\\
a= \dfrac{17}{9}\\\\\\\\\
\boxed{Resposta:~~a= \frac{17}{9}}](https://tex.z-dn.net/?f=x%3Da%5C%5C%5C%5C%5C%0Ay%3D-2%5C%5C%5C%5C%5C%0Az%3D1-2a%5C%5C%5C%5C%5C%5C%5C%5C%0ASubstituindo%7E%7Ena%7E%7Eequac%5C%7Eao%21%5C%5C%5C%5C%5C%5C%5C%0A%0A5%28a%29%2B%28-2%29-2%281-2a%29%3D13%5C%5C%5C%5C%5C%5C%5C%0A5a-2-2%2B4a%3D13%5C%5C%5C%5C%5C%5C%5C%0A5a-4%2B4a%3D13%5C%5C%5C%5C%5C%5C%0A5a%2B4a%3D13%2B4%5C%5C%5C%5C%5C%5C%0A9a%3D17%5C%5C%5C%5C%5C%5C%5C%0Aa%3D+%5Cdfrac%7B17%7D%7B9%7D%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7BResposta%3A%7E%7Ea%3D+%5Cfrac%7B17%7D%7B9%7D%7D++%0A%0A%0A%0A%0A%0A "x=a\\\\\
y=-2\\\\\
z=1-2a\\\\\\\\
Substituindo~~na~~equac\~ao!\\\\\\\
5(a)+(-2)-2(1-2a)=13\\\\\\\
5a-2-2+4a=13\\\\\\\
5a-4+4a=13\\\\\\
5a+4a=13+4\\\\\\
9a=17\\\\\\\
a= \dfrac{17}{9}\\\\\\\\\
\boxed{Resposta:~~a= \frac{17}{9}}")
Bom dia!
Bons estudos!
Solução!
Sendo!
Bom dia!
Bons estudos!
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