Question

решите систему уравнений ​

Answer 1

$\displaystyle\bf\\\left \{ {{3x-5y=4} \atop {9x^{2} +9x+25y^{2} -10y-30xy=18}} \right.\\\\\\\left \{ {{3x-5y=4} \atop {(9x^{2} -30xy+25y^{2} )+(9x-10y)=18}} \right. \\\\\\\left \{ {{3x-5y=4} \atop {\Big[(3x)^{2} -2\cdot 3x\cdot 5y+(5y)^{2} \Big]+9x-10y=18}} \right. \\\\\\\left \{ {{3x-5y=4} \atop {(3x-5y)^{2} +9x-10y=18}} \right. \\\\\\\left \{ {{3x-5y=4} \atop {4^{2} +9x-10y=18}} \right.$

$\displaystyle\bf\\\left \{ {{3x-5y=4} \ |\cdot(-2) \atop {9x-10y=2}} \right.\\\\\\+\left \{ {{-6x+10y=-8} \atop {9x-10y=2}} \right.\\ ----------\\3x=-6\\\\x=-2\\\\5y=3x-4=3\cdot(-2)-4=-6-4=-10\\\\y=-10:5=-2\\\\Otvet \ : \ \Big(-2 \ ; \ -2\Big)$