Question

Помогитерешить, плиз. Даю 10 балов​

Answer 1

Ответ:

1)x=2, y=-1; 2)x=3, y=5; 3) $x_{1}=5, y_{1}=7; x_{2}=-7, y_{2}=-5$

Объяснение:

$1)\left \{ {{4x+3y=5} \atop {y-2x=-5}} \right. \left \{ {{4x+3y=5} \atop {y=-5+2x}} \right.\left \{ {{4x+3(-5+2x)=5} \atop {y=-5+2x}} \right.  \left \{ {{10x-15=5} \atop {y=-5+2x}} \right. \left \{ {{10x=20} \atop {y=-5+2x}} \right. \left \{ {{x=2} \atop {y=-5+4}} \right. \left \{ {{x=2} \atop {y=-1}} \right.$

$2)\left \{ {{5x+y=20} \atop {2x-y=1}} \right. \left \{ {{y=20-5x} \atop {2x-y=1}} \right. \left \{ {{y=20-5x} \atop {2x-20+5x=1}} \right. \left \{ {{y=20-5x} \atop {7x=21}} \right \left \{ {{y=20-15} \atop {x=3}} \right. \left \{ {{y=5} \atop {x=3}} \right.$

$3)\left \{ {{x^2+y^2=74} \atop {x-y=2}} \right. \left \{ {{x^2+y^2=74} \atop {x=2+y}} \right. \left \{ {{(2+y)^2+y^2=74} \atop {x=2+y}} \right. \left \{ {{4+4y+y^2+y^2=74} \atop {x=2+y}} \right. \left \{ {{2y^2+4y-70=0} \atop {x=2+y}} \right. \\\\2y^2+4y-70=0\\\\y^2+2y-35=0\\\\D=b^2-4ac=4+140=144=12^2\\\\x_{1}=\frac{-2+12}{2}=5\\\\x_{2}=\frac{-2-12}{2}=-7\\\\\left \{ {{x_{1}=5 } \atop {y_{1}=7}} \right. \left \{ {{x_{2}=-7} \atop {y_{2}=-5}} \right.$