Question

Решите системы уравнений: 1) 4x-3y=-1 x-5y=4 2) 2xy=5 2x+y=6

Answer 1

$1)\ \ \left\{\begin{array}{l}4x-3y=-1\\x-5y=4\, |\cdot (-4)\end{array}\right\ \oplus \ \left\{\begin{array}{l}17y=-17\\x-5y=4\end{array}\right\ \ \left\{\begin{array}{l}y=-1\\x=5y+4\end{array}\right\ \ \left\{\begin{array}{ccc}y=-1\\x=-1\end{array}\right\\\\\\Otvet:\ \ (-1\, ;\, -1)\ .$

$2)\ \ \left\{\begin{array}{l}2xy=5\\2x+y=6\end{array}\right\ \ \left\{\begin{array}{ccc}2x(6-2x)=5\\y=6-2x\end{array}\right\ \ \left\{\begin{array}{l}12x-4x^2-5=0\\y=6-2x\end{array}\right\\\\\\\left\{\begin{array}{l}x_1=\dfrac{1}{2}\ ,\ x_2=\dfrac{5}{2}\\y_1=5\ ,\ y_2=1\end{array}\right\ \ \ \ Otvet:\ \ (0,5\ ;\ 5\, )\ ,\ \ (2,5\ ;\, 1\, )\ .$