Question

решить систему уравнений x/y+5y/x=-6 2x+7=6

Answer 1

 

$x/y+5y/x=-6\\ 2x+7=6\\ x/y+5y/x=-6 | xy, x <> 0, y <> 0\\ x^2+5y^2 = -6xy\\ x^2 + 6xy + 5y^2 = 0\\ x^2 + xy + 5xy + 5y^2 = 0\\ x(x+y) + 5y(x + y) = 0\\ (x + y)(x + 5y) = 0\\ x + y = 0, x + 5y = 0$

 

$1) x = -y\\ 2x+7=6\ -2y = -1\\ y = 1/2\\ x = -1/2\\ 2) x = -5y\\ 2x+7=6\\ -10y = -1\\ y = 1/10\\ x = -1/2\\ (-1/2, 1/2), (-1/2, 1/10)$