Question

Решите систему уравнений {y-5x=1 ; y²-13x=23

Answer 1

$\left \{ {{y-5x=1} \atop {y^{2}-13x =23}} \right. \\y-5x=1\\y=1+5x$- подстановка

$(1+5x)^{2}-13x=23\\ 1+10x+25x^{2} -13x-23=0\\25x^{2} -3x-22=0\\D=(-3)^{2} -4*25*(-22)=9+2200=2209\\x_{1} =\frac{3+\sqrt{2209} }{2*25}=\frac{3+47}{50}=\frac{50}{50}=1\\ x_{2} =\frac{3-\sqrt{2209} }{2*25}=\frac{3-47}{50}=-\frac{44}{50}=-0,88\\ y_1=1+5*1=1+5=6\\ y_2=1-5*0,88=1-4,4=-3,4$

Ответ:

$\left \{ {{x_1=1} \atop {y_1=6}} \right. \left \{ {{x_2=-0,88} \atop {y_2=-3,4}} \right.$