Question

Seja a matriz quadrada de ordem 2 formada pelos coeficientes das incógnitas do sistema linear, 3x+2y=1
-x + 4y=5

Answer 1

Resposta:

x=-3/7

y=8/7

Explicação passo-a-passo:

3x+2y=1

-x+4y=5$\left[\begin{array}{ccc}3&2&|1\\-1&4&|5\end{array}\right] L2=L2+\frac{1}{3}L1 \\\left[\begin{array}{ccc}3&2&|1\\0&\frac{14}{3} &|\frac{16}{3} \end{array}\right]$

$3x+2y=1\\0+\frac{14}{3}y=\frac{16}{3}$

logo

$y=\frac{\frac{16}{3} }{\frac{14}{3} }$

simplificando

$y=\frac{16}{14} \\y=\frac{8}{7} \\3x+2(\frac{8}{7} )=1\\3x+\frac{16}{7}=1\\3x=1-\frac{16}{7} \\3x=\frac{7-16}{7} \\3x=\frac{-9}{7} \\x=\frac{-3}{7}$