Question

Решите системы уравнений: 
1){1/2+1/y=5/4
xy=4
2) {y-2x+6=0
6y=x²
3) {2y-x²=1
2y+x²=19

Answer 1

$2) left { {{y-2x+6=0} atop {6y=x^{2} }} right. \ left { {{frac{ x^{2} }{6} -2x+6=0} atop {y= frac{ x^{2} }{6} }} right. \ left { {{ x^{2} -12x+36=0} atop {y= frac{ x^{2} }{6} }} right. \ left { {{( x-6)^{2}} atop {y= frac{ x^{2} }{6} }} right.$
$left { {{ x=6} atop {y= frac{ 6^{2} }{6} }} right.$
Ответ. х=6 у=6
$2) left { {{2y- x^{2} =1} atop {2y+ x^{2} =19}} right. \ left { {{x^{2}=2y- 1} atop { x^{2} =19-2y}} right.$
Приравниваем правые части
2у - 1 =19 - 2у
2у + 2у = 19 + 1
4у = 20
 у= 20 : 4
 у= 5
х²=2у - 1 = 2·5 - 1 = 9
х=3    или    х =-3
Ответ. (-3;5) (3;5)