Exercicios de Matematica 9 Ano - Sistema de Equações - Exercicio 2

Exercicios de Matematica 9 Ano - Sistema de Equações

Resolva e classifique os seguintes sistemas:

$\left\{ {\begin{array}{*{20}{c}} {x - 6y = - 19} \\ {x + y - 2 = 0} \end{array}} \right.$

$\left\{ {\begin{array}{*{20}{c}} {3x + 2y = 5} \\ {y = \frac{{5 - 3x}}{2}} \end{array}} \right.$

$\left\{ {\begin{array}{*{20}{c}} {7y = 2x + 6} \\ {x = \frac{7}{2}y + 2} \end{array}} \right.$

Resolução dos Exercícios de Matemática de Sistema de Equações:

$\left\{ {\begin{array}{*{20}{c}} {x - 6y = - 19} \\ {x + y - 2 = 0} \end{array}} \right. \Leftrightarrow \left\{ {\begin{array}{*{20}{c}} {2 - y - 6y = - 19} \\ {x = 2 - y} \end{array}} \right. \Leftrightarrow$

$\Leftrightarrow \left\{ {\begin{array}{*{20}{c}} { - 7y = - 21} \\ {x = 2 - y} \end{array}} \right. \Leftrightarrow \left\{ {\begin{array}{*{20}{c}} {y = 3} \\ {x = 2 - 3} \end{array}} \right. \Leftrightarrow \left\{ {\begin{array}{*{20}{c}} {y = 3} \\ {x = - 1} \end{array}} \right.$

Sistema possível e determinado $S = \left\{ {\left( {-1, 3} \right)} \right\}$

$\left\{ {\begin{array}{*{20}{c}} {3x + 2y = 5} \\ {y = \frac{{5 - 3x}}{2}} \end{array}} \right. \Leftrightarrow \left\{ {\begin{array}{*{20}{c}} {3x + 2\left( {\frac{{5 - 3x}}{2}} \right) = 5} \\ {y = \frac{{5 - 3x}}{2}} \end{array}} \right. \Leftrightarrow$

$\Leftrightarrow \left\{ {\begin{array}{*{20}{c}} {3x + 5 - 3x = 5} \\ {y = \frac{{5 - 3x}}{2}} \end{array}} \right. \Leftrightarrow \left\{ {\begin{array}{*{20}{c}} {0x = 0} \\ {y = \frac{{5 - 3x}}{2}} \end{array}} \right.$

Sistema possível e indeterminado $S = \left\{ {\left( {x; \frac{5-3x}{2}} \right)} \right\}$

$\left\{ {\begin{array}{*{20}{c}} {7y = 2x + 6} \\ {x = \frac{7}{2}y + 2} \end{array}} \right. \Leftrightarrow \left\{ {\begin{array}{*{20}{c}} {7y = 2\left( {\frac{7}{2}y + 2} \right) + 6} \\ {x = \frac{7}{2}y + 2} \end{array}} \right. \Leftrightarrow$

$\Leftrightarrow \left\{ {\begin{array}{*{20}{c}} {7y = 7y + 4 + 6} \\ {x = \frac{7}{2}y + 2} \end{array}} \right. \Leftrightarrow \left\{ {\begin{array}{*{20}{c}} {0y = 10} \\ {x = \frac{7}{2}y + 2} \end{array}} \right.$