A solução do sistema
Equações literais e sistemas: Matematicamente Falando 8 - Pág. 202 Ex. 1
Enunciado
Encontra mentalmente a solução de cada um dos sistemas de equações.
Explica como fizeste.
\(\left\{ {\begin{array}{*{20}{l}}{x = \frac{1}{2}}\\{2x + y = 7}\end{array}} \right.\)
\(\left\{ {\begin{array}{*{20}{l}}{x + y = 11}\\{\frac{y}{2} = 5}\end{array}} \right.\)
\(\left\{ {\begin{array}{*{20}{l}}{x – y = 1}\\{y – 2 = 0}\end{array}} \right.\)
\(\left\{ {\begin{array}{*{20}{l}}{y = x + 5}\\{y = 2x}\end{array}} \right.\)
Resolução
| 1. | \[\begin{array}{*{20}{c}}{\left\{ {\begin{array}{*{20}{l}}{x = \frac{1}{2}}\\{2x + y = 7}\end{array}} \right.}& \Leftrightarrow &{\left\{ {\begin{array}{*{20}{l}}{x = \frac{1}{2}}\\{y = 6}\end{array}} \right.}\end{array}\] | \(\begin{array}{*{20}{c}}{2 \times \frac{1}{2} + y = 7}& \Leftrightarrow &{y = 6}\end{array}\) 
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| 2. | \(\begin{array}{*{20}{c}}{\left\{ {\begin{array}{*{20}{l}}{x + y = 11}\\{\frac{y}{2} = 5}\end{array}} \right.}& \Leftrightarrow &{\left\{ {\begin{array}{*{20}{l}}{y = 10}\\{x = 1}\end{array}} \right.}\end{array}\) | \(\begin{array}{*{20}{c}}{\frac{y}{2} = 5}& \Leftrightarrow &{y = 10}\\{x + 10 = 11}& \Leftrightarrow &{x = 1}\end{array}\)
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| 3. | \(\begin{array}{*{20}{c}}{\left\{ {\begin{array}{*{20}{l}}{x – y = 1}\\{y – 2 = 0}\end{array}} \right.}& \Leftrightarrow &{\left\{ {\begin{array}{*{20}{l}}{y = 2}\\{x = 3}\end{array}} \right.}\end{array}\) | \(\begin{array}{*{20}{c}}{y – 2 = 0}& \Leftrightarrow &{y = 2}\\{x – 2 = 1}& \Leftrightarrow &{x = 3}\end{array}\)
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| 4. | \(\begin{array}{*{20}{c}}{\left\{ {\begin{array}{*{20}{l}}{y = x + 5}\\{y = 2x}\end{array}} \right.}& \Leftrightarrow &{\left\{ {\begin{array}{*{20}{l}}{x = 5}\\{y = 10}\end{array}} \right.}\end{array}\) | \(\begin{array}{*{20}{c}}{2x = x + 5}& \Leftrightarrow &{x = 5}\\{y = 2 \times 5}& \Leftrightarrow &{y = 10}\end{array}\)
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