Question

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$left { {{x^2 + 2x - 5y = -5} atop {x^2 +y^2 +2x - 10y = -9}} right.$

Answer 1

$left { {{x^2+2x-5y=-5} atop {x^2+y^2+2x-10y=-9}} right. ; left { {{(x+1)^2-1-5y=-5} atop {(x+1)^2-1+(y-5)^2-25=-9}} right. ; left { {{(x+1)^2=5y-4} atop {(x+1)^2=17-(y-5)^2}} right. \\5y-4=17-(y-5)^2\\5y-4=17-(y^2-10y+25)\\y^2-5y+4=0; ; to ; ; ; y_1=1; ,; y_2=4; ; (teorema; Vieta)\\(x+1)^2=17-(y-5)^2; ; to$

$a); ; y=1; ; to ; ; (x+1)^2=17-(-4)^2=17-16=1\\x+1=pm 1; ; Rightarrow ; ; x_1=1-1=0; ,; ; x_2=-1-1=-2\\b); ; y=4; ; to ; ; (x+1)^2=17-(-1)^2=16$

$x+1=pm 4; ; Rightarrow x_3=4-1=3; ,; ; x_4=-4-1=-5\\Otvet:; ; (0,1); ,; (-2,1); ,; (3,4); ,; (-5,4); .$