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)