\nEnunciado<\/b><\/span><\/p>\n
Representa graficamente as equa\u00e7\u00f5es e classifica cada sistema:<\/p>\n
- \n
- \\(\\left\\{ \\begin{array}{*{35}{l}}
\ny=x-7\u00a0 \\\\
\nx=y+3\u00a0 \\\\
\n\\end{array} \\right.\\)
\n\u00ad<\/li>\n - \\(\\left\\{ \\begin{array}{*{35}{l}}
\ny=2x+2\u00a0 \\\\
\nx=2y+2\u00a0 \\\\
\n\\end{array} \\right.\\)
\n\u00ad<\/li>\n - \\(\\left\\{ \\begin{array}{*{35}{l}}
\ny=x+2\u00a0 \\\\
\nx=y-2\u00a0 \\\\
\n\\end{array} \\right.\\)<\/li>\n<\/ol>\nResolu\u00e7\u00e3o >><\/a><\/span><\/div><\/div>\n\n\nResolu\u00e7\u00e3o<\/b><\/span><\/p>\n- \n
- \u00a0Resolvendo cada uma das equa\u00e7\u00f5es em ordem a y, temos: \\[\\begin{array}{*{35}{l}}
\n\\left\\{ \\begin{array}{*{35}{l}}
\ny=x-7\u00a0 \\\\
\nx=y+3\u00a0 \\\\
\n\\end{array} \\right. & \\Leftrightarrow\u00a0 & \\left\\{ \\begin{array}{*{35}{l}}
\ny=x-7\u00a0 \\\\
\ny=x-3\u00a0 \\\\
\n\\end{array} \\right.\u00a0 \\\\
\n\\end{array}\\]
\nAs retas s\u00e3o estritamente paralelas, pois possuem iguais declives (${{k}_{1}}=1$ e ${{k}_{2}}=1$) e ordenadas na origem diferentes (${{b}_{1}}=-7$ e ${{b}_{2}}=-3$).
\nLogo, o sistema \u00e9 imposs\u00edvel.
\n![\"\"](\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/sistG1.gif\" "\\"Gr\u00e1fico\\"")
<\/a>\u00ad<\/li>\n- Resolvendo cada uma das equa\u00e7\u00f5es em ordem a y, temos: \\[\\begin{array}{*{35}{l}}
\n\\left\\{ \\begin{array}{*{35}{l}}
\ny=2x+2\u00a0 \\\\
\nx=2y+2\u00a0 \\\\
\n\\end{array} \\right. & \\Leftrightarrow\u00a0 & \\left\\{ \\begin{array}{*{35}{l}}
\ny=2x+2\u00a0 \\\\
\ny=\\frac{1}{2}x-1\u00a0 \\\\
\n\\end{array} \\right.\u00a0 \\\\
\n\\end{array}\\]
\nAs retas s\u00e3o concorrentes, pois possuem\u00a0declives diferentes (${{k}_{1}}=2$ e ${{k}_{2}}=\\frac{1}{2}$).
\nLogo, o sistema \u00e9 poss\u00edvel e determinado (com uma solu\u00e7\u00e3o).
\n![\"\"](\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/sistG2.gif\" "\\"Gr\u00e1fico\\"")
<\/a>\u00ad<\/li>\n- Resolvendo cada uma das equa\u00e7\u00f5es em ordem a y, temos: \\[\\begin{array}{*{35}{l}}
\n\\left\\{ \\begin{array}{*{35}{l}}
\ny=x+2\u00a0 \\\\
\nx=y-2\u00a0 \\\\
\n\\end{array} \\right. & \\Leftrightarrow\u00a0 & \\left\\{ \\begin{array}{*{35}{l}}
\ny=x+2\u00a0 \\\\
\ny=x+2\u00a0 \\\\
\n\\end{array} \\right.\u00a0 \\\\
\n\\end{array}\\]
\nAs retas s\u00e3o coincidentes, pois possuem iguais declives (${{k}_{1}}=1$ e ${{k}_{2}}=1$) e iguais ordenadas na origem (${{b}_{1}}=2$ e ${{b}_{2}}=2$).
\nLogo, o sistema \u00e9 poss\u00edvel e indeterminado (uma infinidade de solu\u00e7\u00f5es).
\n![\"\"](\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2011\/10\/sistG3.gif\" "\\"Gr\u00e1fico\\"")
<\/a><\/li>\n<\/ol>\n - Resolvendo cada uma das equa\u00e7\u00f5es em ordem a y, temos: \\[\\begin{array}{*{35}{l}}
- \u00a0Resolvendo cada uma das equa\u00e7\u00f5es em ordem a y, temos: \\[\\begin{array}{*{35}{l}}