Question

3x+2y=-7
5x-2y=5
Resolver por determinantes

Answer 1

Al resolver por determinante se obtiene:

x = -1/4

y = -25/8

Explicación:

Para resolver el sistema de ecuaciones de 2x2;

x_n = det(B_n)/det(A)

siendo;

B_n: matriz de términos independientes.

$A=\left[\begin{array}{cc}3&2\\5&-2\end{array}\right]$

det(A);

$det(A)=\left[\begin{array}{cc}3&2\\5&-2\end{array}\right]$

= 3(-2)-2(5)

= -6 - 10

det(A) = -16

det(B₁) ;

$=\left[\begin{array}{cc}-7&2\\5&-2\end{array}\right]$

= (-7)(-2)-(5)(2)

= 14 - 10

det(B₁) = 4

x = det(B₁)/det(A)

x = 4/-16

x = -1/4

det(B₂);

$=\left[\begin{array}{cc}3&-7\\5&5\end{array}\right]$

=(3)(5)-(-7)(5)

= 15 + 35

det(B₂) = 50

y = det(B₂)/det(A)

y = 50/-16

y = -25/8