Question

решить систему уравнений чтоб все было подробно

Answer 1

Решаем методом подстановки . Из одного уравнения выражаем переменную через другую и подставляем выражение во второе уравнение .

$1)\ \ \left\{\begin{array}{l}x-2y=-9\\y=3x+2\end{array}\right\ \ \left\{\begin{array}{l}x-2(3x+2)=-9\\y=3x+2\end{array}\right\ \ \left\{\begin{array}{l}x-6x-4=-9\\y=3x+2\end{array}\rightleft\{\begin{array}{l}-5x=-5\\y=3x+2\end{array}\right\ \ \left\{\begin{array}{l}x=1\\y=3x+2\end{array}\right\ \ \left\{\begin{array}{l}x=1\\y=3+2\end{array}\right\ \ \left\{\begin{array}{l}x=1\\y=5\end{array}\rightOtvet:\ (1;5)\ .$

$2)\ \ \left\{\begin{array}{l}2y+x=-8\\5x-4y=16\end{array}\right\ \ \left\{\begin{array}{l}x=-2y-8\\5(-2y-8)-4y=16\end{array}\right\ \ \left\{\begin{array}{l}x=-2y-8\\-14y-40=16\end{array}\rightleft\{\begin{array}{l}x=-2y-8\\-14y=56\end{array}\right\ \ \left\{\begin{array}{l}x=-2\cdot (-4)-8\\y=-4\end{array}\right\ \ \left\{\begin{array}{l}x=0\\y=-4\end{array}\right\ \ \ Otve:\ (0;-4)\ .$

$3)\ \ \left\{\begin{array}{l}4-x=y+5\\y-4x=14\end{array}\right\ \ \left\{\begin{array}{l}4-x=4x+14+5\\y=4x+14\end{array}\right\ \ \left\{\begin{array}{l}5x=-15\\y=4x+14\end{array}\rightleft\{\begin{array}{l}x=-3\\y=-4\cdot 3+14\end{array}\right\ \ \left\{\begin{array}{l}x=-3\\y=2\end{array}\right\ \ \ \ \ Otvet:\ (-3;2)\ .$

$4)\ \ \left\{\begin{array}{l}3x+y=14\\5x=3y\end{array}\right\ \ \left\{\begin{array}{l}y=14-3x\\5x=3(14-3x)\end{array}\right\ \ \left\{\begin{array}{l}y=14-3x\\5x=42-9x\end{array}\rightleft\{\begin{array}{l}y=14-3x\\14x=42\end{array}\right\ \ \left\{\begin{array}{l}y=14-3\cdot 3\\x=3\end{array}\right\ \ \left\{\begin{array}{l}y=5\\x=3\end{array}\right\ \ \ \ Otvet:\ (3;5)\ .$

$5)\ \ \left\{\begin{array}{l}7x-2y=28\\x+y=-5\end{array}\right\ \ \left\{\begin{array}{l}7x-2(-5-x)=28\\y=-5-x\end{array}\right\ \ \left\{\begin{array}{l}9x+10=28\\y=-5-x\end{array}\rightleft\{\begin{array}{l}9x=18\\y=-5-x\end{array}\right\ \ \left\{\begin{array}{l}x=2\\y=-5-2\end{array}\right\ \ \left\{\begin{array}{l}x=2\\y=-7\end{array}\right\ \ \ \ Otvet:\ (2;-7)$

$6)\ \ \left\{\begin{array}{l}4y=x+46\\3x+2y=7\end{array}\right\ \ \left\{\begin{array}{l}x=4y-46-\\3(4y-46)+2y=7\end{array}\right\ \ \left\{\begin{array}{l}x=4y-46\\12y-138+2y=7\end{array}\rightleft\{\begin{array}{l}x=4y-46\\14y=145\end{array}\right\ \ \left\{\begin{array}{l}x=4\cdot \dfrac{145}{14}-46\\y=\dfrac{145}{14}\end{array}\right\ \ \left\{\begin{array}{l}\ x=-\dfrac{32}{7}\\y=\dfrac{145}{14}\end{array}\right\ \ \ Otvet:\ \Big(-4\dfrac{4}{7}\ ;10\dfrac{5}{14}\ \Big)\ .$