Question

Sabendo que :

x = y = z

10 15 20

2x + 3y - z = 9

Qual o valor de x , y e z ?

Answer 1

Resposta:

Os valores de x, y e z são respectivamente 2, 3 e 4.

Explicação passo-a-passo:

Vamos resolver por substituição, com base nas equações:

$\dfrac{x}{10}=\dfrac{y}{15}=\dfrac{z}{20}\\\\2x+3y-z=9\\\\\\\dfrac{x}{10}=\dfrac{y}{15}\longrightarrow \boxed{x=\dfrac{10y}{15}}\\\\\\\dfrac{z}{20}=\dfrac{y}{15}\longrightarrow \boxed{z=\dfrac{20y}{15}}\\\\\\\\2\times\left(\dfrac{10y}{15}\right)+3y-\left(\dfrac{20y}{15}\right)=9\\\\\dfrac{20y}{15}\right)+3y-\dfrac{20y}{15}=9\\\\3y=9 \longrightarrow y=\dfrac{9}{3}=3\\\\\boxed{y=\bf{3}}\\\\\\x=\dfrac{10y}{15}=\dfrac{10\times3}{15}=\dfrac{30}{15} = 2\\\\\boxed{x=\bf{2}}$

$z=\dfrac{20y}{15} =\dfrac{20\times3}{15}=\dfrac{60}{15} = 4\\\\\boxed{z=\bf{4}}$

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