Calcule x e y na proporção x/y = 2/3, sabendo-se que x + y = 10
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Boa noite Capivara!
Solução!
Esse exercicio pode ser resolvido como um sistema linear com duas variaveis.
![x+y=10\\\\\
\dfrac{x}{y} = \dfrac{2}{3}\\\\\\\
Fazendo!\\\\\
3x=2y\\\\\
x= \dfrac{2y}{3}\\\\\\
Substituindo~~na~~primeira~~equac\~ao . \\\\\\\
\dfrac{2y}{3}+y=10\\\\\\\
2y+3y=30\\\\\
5y=30\\\\\\\
y= \dfrac{30}{5}\\\\\\\
\boxed{y=6}](https://tex.z-dn.net/?f=x%2By%3D10%5C%5C%5C%5C%5C%0A+%5Cdfrac%7Bx%7D%7By%7D+%3D+%5Cdfrac%7B2%7D%7B3%7D%5C%5C%5C%5C%5C%5C%5C%0AFazendo%21%5C%5C%5C%5C%5C%0A3x%3D2y%5C%5C%5C%5C%5C%0Ax%3D+%5Cdfrac%7B2y%7D%7B3%7D%5C%5C%5C%5C%5C%5C%0ASubstituindo%7E%7Ena%7E%7Eprimeira%7E%7Eequac%5C%7Eao+.+%5C%5C%5C%5C%5C%5C%5C%0A%0A%5Cdfrac%7B2y%7D%7B3%7D%2By%3D10%5C%5C%5C%5C%5C%5C%5C%0A2y%2B3y%3D30%5C%5C%5C%5C%5C%0A5y%3D30%5C%5C%5C%5C%5C%5C%5C%0Ay%3D+%5Cdfrac%7B30%7D%7B5%7D%5C%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7By%3D6%7D+%0A "x+y=10\\\\\
\dfrac{x}{y} = \dfrac{2}{3}\\\\\\\
Fazendo!\\\\\
3x=2y\\\\\
x= \dfrac{2y}{3}\\\\\\
Substituindo~~na~~primeira~~equac\~ao . \\\\\\\
\dfrac{2y}{3}+y=10\\\\\\\
2y+3y=30\\\\\
5y=30\\\\\\\
y= \dfrac{30}{5}\\\\\\\
\boxed{y=6}")
![y=6\\\\\
x= \dfrac{2y}{3}\\\\\\\
x= \dfrac{2(6)}{3}\\\\\\\
x= \dfrac{12}{3}\\\\\\\
\boxed{x=4}](https://tex.z-dn.net/?f=+y%3D6%5C%5C%5C%5C%5C%0A%0A%0Ax%3D+%5Cdfrac%7B2y%7D%7B3%7D%5C%5C%5C%5C%5C%5C%5C%0Ax%3D+%5Cdfrac%7B2%286%29%7D%7B3%7D%5C%5C%5C%5C%5C%5C%5C%0Ax%3D+%5Cdfrac%7B12%7D%7B3%7D%5C%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7Bx%3D4%7D "y=6\\\\\
x= \dfrac{2y}{3}\\\\\\\
x= \dfrac{2(6)}{3}\\\\\\\
x= \dfrac{12}{3}\\\\\\\
\boxed{x=4}")
Boa noite!
Bons estudos!
Solução!
Esse exercicio pode ser resolvido como um sistema linear com duas variaveis.
Boa noite!
Bons estudos!
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