Question

даю 50 баллов
$1$
плиз​

Answer 1

Ответ:

Объяснение:

$\displaystyle\\\left \{ {{\dfrac{y}{x}- \dfrac{x}{y} =\dfrac{16}{15} } \atop {4y-5x=15}} \right. ;~~~~~~~~~~~~x\neq 0;y\neq 0$

рассмотрим 1 уравнение

$\displaystyle\\15y^2-15x^2=16xy\\15y^2-16xy-15x^2=0\\15y^2+9xy-25xy-15x^2=0\\3y(5y+3x)-5x(5y+3x)=0\\(5y+3x)(3y-5x)=0$

$\displaystyle\\1)~\left \{ {{5y+3x=0} \atop {4y-5x=15}} \right. ;\left \{ {{y=-0,6x} \atop {4\cdot(-0,6)x-5x=15}} \right. ;\left \{ {{y=-0,6x} \atop {-7,4x=15}} \right. \\\\\\\left \{ {{y=-0,6x} \atop {x=-\dfrac{15}{7,4} }} \right. ;\left \{ {{y=-\dfrac{3}{5}x } \atop {x=-\dfrac{150}{74} }} \right. ;\left \{ {{y=-\dfrac{3}{5}\cdot\bigg(-\dfrac{75}{37}\bigg) } \atop {x=-\dfrac{75}{37} }} \right. \\\\\\\left \{ {{y=\dfrac{45}{37} } \atop {x=-\dfrac{75}{37} }} \right.$

$2)\displaystyle\\~\left \{ {{3y-5x=0} \atop {4y-5x=15}} \right. ;\left \{ {{x=0,6y} \atop {4y-5\cdot0,6y=15}} \right. ;\left \{ {{x=0,6\cdot15} \atop {y=15}} \right. ;\left \{ {{x=9} \atop {y=15}} \right.$

Ответ:

$\displaystyle\\(9;15)~~\bigg(-2\frac{1}{37} ;1\frac{8}{37} \bigg)$