Question

Resolver por el método de Cramer
0.2x + 0.1y = 1.1
x/18 + y/6 = 1
Ayuda Porfaa

Answer 1

Respuesta:

Explicación paso a paso:

Método de Cramer:

Matriz ( A ):

$A = \left[\begin{array}{ccc}0.2&0.1&\\\frac{1}{18} &\frac{1}{6} &\\\end{array}\right]$

Buscamos el determinante de la matriz A.

$|A| = \left[\begin{array}{ccc}0.2&0.1&\\\frac{1}{18} &\frac{1}{6} &\\\end{array}\right] = (0.2)(\frac{1}{6} ) - ( 0.1 ) ( \frac{1}{18} ) = \frac{0.2}{6} -\frac{0.1}{18} = \frac{\frac{2}{10} }{6} -\frac{\frac{1}{10} }{18} = \frac{2}{60} -\frac{1}{180}$

$|A| = \frac{1}{36}$

Buscamos el determinante respecto a la incógnita " x ".

$|A|_{x} = \left[\begin{array}{ccc}1.1&0.1&\\1&\frac{1}{6} &\\\end{array}\right] = (1.1)(\frac{1}{6} )-( 0.1) (1) = \frac{1.1}{6} - \frac{0.1}{1} = \frac{\frac{11}{10} }{6} -\frac{\frac{1}{10} }{1} = \frac{11}{60} -\frac{1}{10}$

$|A|_{x} = \frac{1}{12}$

Buscamos el determinante respecto a la incógnita " y ".

$|A|_{y} = \left[\begin{array}{ccc}0.2&1.1&\\\frac{1}{18} &1&\\\end{array}\right] = (0.2)(1)- (1.1)(\frac{1}{18} ) = \frac{0.2}{1} -\frac{1.1}{18} = \frac{\frac{2}{10} }{1} -\frac{\frac{11}{10} }{18} = \frac{2}{10} - \frac{11}{180}$

$|A|_{y} = \frac{5}{36}$

Buscamos los valores de las incógnitas:

$x = \frac{|A|_{x} }{|A|} = \frac{\frac{1}{12} }{\frac{1}{36} } = \frac{36}{12} = 3$

$y = \frac{|A|_{y} }{|A|} = \frac{\frac{5}{36} }{\frac{1}{36} } = \frac{180}{36} = 5$

RESPUESTA:

    $x = 3$    ;  $y = 5$