26А. При каких значениях параметра a система уравнений \(\left\{ {\begin{array}{*{20}{c}} {2x + \left( {a-1} \right)\,y = 3,\,\,\,} \\ {\left( {a + 1} \right)\,\,x + 4y = -3} \end{array}} \right.\) не имеет решений?
Решение
Система не будет иметь решений, если:
\(\dfrac{2}{{a + 1}} = \dfrac{{a-1}}{4} \ne \dfrac{3}{{-3}}\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\left\{ {\begin{array}{*{20}{c}}{\dfrac{2}{{a + 1}} = \dfrac{{a-1}}{4},}\\{\dfrac{{a-1}}{4} \ne \dfrac{3}{{-3}}\,\,\,\,\,\,}\end{array}} \right.\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left\{ {\begin{array}{*{20}{c}}{{a^2} = 9,\,\,\,\,\,\,\,}\\{a-1 \ne -4}\end{array}} \right.\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\left\{ {\begin{array}{*{20}{c}}{\left[ {\begin{array}{*{20}{c}}{a = 3,}\\{a = -3}\end{array}} \right.}\\{a \ne -3}\end{array}} \right.\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,a = 3.\)
Ответ: 3.