Question

o par (x,y) que satisfaz o sistema de equaçoes lineares { 2x+3y=6 . 3x-2y=5 é:

Answer 1

Resposta:

$S=\left\{x=\dfrac{27}{13},\ y=\dfrac{8}{13}\right\}$

Explicação passo-a-passo:

$\left \{ {2x+3y=6} \atop {3x-2y=5}} \right.$

Por substituição:

Isolando y na equação I:

$2x+3y=6\\\\3y=6-2x\\\\y=\dfrac{6-2x}3$

Substituindo y na equação II e isolando x:

$3x-2\dfrac{6-2x}3=5\\\\3x+\dfrac{4x-12}3=5\\\\\dfrac{9x+4x-12}3=5\\\\\dfrac{13x-12}3=5\\\\13x-12=5.3\\\\13x=15+12\\\\13x=27\\\\x=\dfrac{27}{13}$

Substituindo x na equação I e isolando y:

$2\dfrac{27}{13}+3y=6\\\\\dfrac{54}{13}+3y=6\\\\3y=6-\dfrac{54}{13}\\\\3y=\dfrac{6.13-54}{13}\\\\3y=\dfrac{78-54}{13}\\\\3y=\dfrac{24}{13}\\\\y=\dfrac{24}{13.3}\\\\y=\dfrac{8.3}{13.3}\\\\y=\dfrac{8}{13}$

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