Question

Questão1 - Encontre o Conjunto Solução do Sistema a seguir:
5x + 2y =70
x + y =20
a) (7, 13)
b) (10, 10)
c) (8, 12)
d) (15, 5)
e) (18, 2)

Answer 1

$\binom{5x + 2y = 70}{x + y = 20} \\ \\ 5x + 2y = 70 \\ - 2x - 2y = - 40 \\ \\ 3x = 30 \: \: \: \: \: \: x = \frac{30}{3} = 10 \\ \\ \\ 10 + y = 20 \\ y = 20 - 10 = 10.$

s = {10, 10}

Answer 2

Sistema de Equação

• Temos o Sistema:

$\large \boxed{\boxed{\sf \left \{ { { 5x+2y=70} \atop {x+y=20}} \right.}}$

Resolvendo o sistema pela Regra de Cramer

Cálculo:

• Determinante das variáveis:

$\boxed{\begin{array}{lr} \\ \large \sf D =\left[\begin{array}{ccc} \sf5&\sf2\\\sf1&\sf1\\\end{array}\right] \\\\\large \sf D=5-2\\\\\large \sf D=3\\\: \end{array}}$

• Determinante do x:

$\boxed{\begin{array}{lr} \\ \large \sf D_{x}=\left[\begin{array}{ccc} \sf70&\sf2\\\sf20&\sf1\\\end{array}\right] \\\\\large \sf D_{x}=70-40\\\\\large \sf D_{x}=30\\\: \end{array}}$

• Determinante do y:

$\boxed{\begin{array}{lr} \\ \large \sf D_{y} =\left[\begin{array}{ccc} \sf5&\sf70\\\sf1&\sf20\\\end{array}\right] \\\\\large \sf D_{y}=100-70\\\\\large \sf D_{y}=30\\\: \end{array}}$

• Divisão dos determinantes:

$\large \boxed{\boxed{\sf x =\dfrac{30}{3} =10}}\\\\\\\large \boxed{\boxed{\sf y=\dfrac{30}{3} =10}}$

Resposta:

• Letra B)

$\huge \boxed{\boxed{\sf S=\{10,10\}}}$

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