Question

помогите срочнно Система Уравнений

Answer 1

( 1 )

$\displaystyle\\\left \{ {{x-y=2} \atop {3x+2y=16}} \right.\\\\\left \{ {{x=2+y} \atop {3*(2+y)+2y=16}} \right. \\\\\left \{ {{x=2+y} \atop {6+3y+2y=16}} \right. \\\\\left \{ {{x=2+y} \atop {3y+2y=16-6}} \right. \\\\\left \{ {{x=2+y} \atop {5y=10}} \right. \\\\\left \{ {{x=2+2} \atop {y=2}} \right. \\\\\left \{ {{x=4} \atop {y=2}} \right.$

( 3 )

$\displaystyle\\\left \{ {{x+y=8} \atop {x-y=7}} \right. \\\\\left \{ {{x=8-y} \atop {8-y-y=7}} \right. \\\\\left \{ {{x=8-y} \atop {-y-y=7-8}} \right. \\\\\left \{ {{x=8-y} \atop {-2y=-1}} \right. \\\\\left \{ {{x=8-0,5} \atop {y=0,5}} \right. \\\\\left \{ {{x=7,5} \atop {y=0,5}} \right.$

( 4 )

$\displaystyle\\\left \{ {{x+y=1} \atop {x-y=-6}} \right. \\\\\left \{ {{x=1-y} \atop {1-y-y=-6}} \right. \\\\\left \{ {{x=1-y} \atop {-y-y=-6-1}} \right. \\\\\left \{ {{x=1-y} \atop {-2y=-7}} \right. \\\\\left \{ {{x=1-3,5} \atop {y=3,5}} \right. \\\\\left \{ {{x=-2,5} \atop {y=3,5}} \right.$

( 5 )

$\displaystyle\\\left \{ {{x+3y=10} \atop {x-y=3}} \right. \\\\\left \{ {{x=10-3y} \atop {10-3y-y=3}} \right. \\\\\left \{ {{x=10-3y} \atop {-3y-y=3-10}} \right. \\\\\left \{ {{x=10-3y} \atop {-4y=-7}} \right. \\\\\left \{ {{x=10-3*1,75} \atop {y=1,75}} \right. \\\\\left \{ {{x=10-5,25} \atop {y=1,75}} \right. \\\\\left \{ {{x=4,75} \atop {y=1,75}} \right.$

( 6 )

$\displaystyle\\\left \{ {{x-2y=-7} \atop {xy=-6}} \right. \\\\\left \{ {{x=-7+2y} \atop {x=\frac{-6}{y} }} \right. \\\\\left \{ {x=-7+2y} \atop {-7+2y=\frac{-6}{y} }} \right. \\\\\\-7+2y=\frac{-6}{y}|*y\\\\y(-7+2y)=\frac{-6y}{y}\\\\-7y+2y^2=-6\\\\2y^2-7y+6=0\\\\D=b^2-4ac=(-7)^2-4*1*6=49-48=1 \\\\y_1=\frac{-b+\sqrt{D} }{2a} =\frac{7+\sqrt{1} }{2*2} =\frac{7+1}{4}=\frac{8}{4}=2\\\\y_2=\frac{-b-\sqrt{D} }{2a} =\frac{7-\sqrt{1} }{2*2} =\frac{7-1}{4}=\frac{6}{4}=1,5$

$\displaystyle\\\left \{ {{x_1=-7+2y} \atop {y_1=2}} \right. \\\\\left \{ {{x_1=-7+2*2} \atop {y_1=2}} \right. \\\\\left \{ {{x_1=-7+4} \atop {y_1=2}} \right. \\\\\left \{ {{x_1=-3} \atop {y_1=2}} \right. \\\\\\\left \{ {{x_2=-7+2y} \atop {y_2=1,5}} \right. \\\\\left \{ {{x_2=-7+2*1,5} \atop {y_2=1,5}} \right. \\\\\left \{ {{x_2=-7+3} \atop {y_2=1,5}} \right. \\\\\left \{ {{x_2=-4} \atop {y_2=1,5}} \right.$