Question

Реши систему уравнений:
x−2/y+4=9/13
(x−2)2+(y+4)2=250/9

Answer 1

$(5 ; \frac{1}{3} ); \: ( - 1 ; \ - \frac{25}{3} )$

Объяснение:

$\frac{x - 2}{y + 4} = \frac{9}{13} \\ (x - 2) {}^{2} + (y + 4) {}^{2} = \frac{250}{9} \\ \\ x - 2 = \frac{9}{13} \cdot(y + 4) \\ \frac{81}{169} (y + 4) {}^{2} + (y + 4) {}^{2} = \frac{250}{9} \\ \\ x = \frac{9(y + 4)}{13} + 2 \\ \frac{250}{169} (y + 4) {}^{2} = \frac{250}{9} < = |y + 4| = \frac{13}{3} \\ \\ |y + 4| = \frac{13}{3} \\ x = \frac{9(y + 4)}{13} + 2 \\ \\ y_1 + 4 = \frac{13 }{3} < = y_1 = \frac{1}{3} \\ x_1 = \frac{9}{13} \cdot \frac{13}{3} + 2 < = x_1= 5 \\ \\ y_2 + 4 = - \frac{13 }{3} < = y_2 = - \frac{25}{3} \\ x_2 = \frac{9}{13} \cdot (- \frac{13}{3} ) + 2 < = x_2= - 1$