Question

Sistema de equações lineares
Método da adição

14x -21y =77
28x -28y = 432

Answer 1

Explicação passo-a-passo:

( 14x - 21y = 77

( 28x - 28y = 432 ÷(2)facilitar o calculo

( 14x - 21y = 77

(14x - 14y =216 ×(-1)

( 14x -21y = 77

(-14 + 14y= - 216

===============(+)

- 7y = - 139 × (-1)

7y = 139

y=139/7

14x - 21y=77

14x - 21× (139/7) = 77

14x - 3.(139)=77

14x - 417=77

14x= 77 + 417

14x =494

x=494/14

x =247/7

S= ( 247/7 e 139/7)

Answer 2

$\sf \begin{cases}\sf 14x -21y =77 \\\\\\ \sf 28x -28y = 432\end{cases}\\\\\\Regra \ de \ \to Cramer\\\\\\M=\begin{pmatrix}\sf 14&-\sf 21\\ \sf 28&-\sf 28\end{pmatrix}\\\\\\{Substitua\:}x{-valores\:da\:coluna\:com\:valores\:da\:coluna\:de\:respostas}\\\\\\M_x=\begin{pmatrix}\sf 77&-\sf 21\\ \sf 432&-\sf 28\end{pmatrix}\\\\\\M_y=\begin{pmatrix}\sf 14&\sf 77\\ \sf 28&\sf 432\end{pmatrix}\\\\\\D=196\\\\D_x=6916\\\\D_y=3892\\\\\\{Resolva\:usando\:a\:regra\:de\:Cramer}$

$\sf \displaystyle x=\frac{D_x}{D},\:y=\frac{D_y}{D},\:z=\frac{D_z}{D}\\\\\\D\:{denota\:o\:determinante}\\\\\\x=\frac{D_x}{D}=\frac{6916}{196}\\\\\\y=\frac{D_y}{D}=\frac{3892}{196}\\\\\\\to \boxed{\sf x=\frac{247}{7},\:y=\frac{139}{7}}$