Question

с самостоятельной с самостоятельной

Answer 1

Уровень "А"

$a)\\\left \{ {{y=3x,} \atop {4x+5y=38;}} \right. \\\left \{ {{y=3x,} \atop {4x+5*3x=38;}} \right.\\\left \{ {{y=3x,} \atop {4x+15x=38;}} \right. \\\left \{ {{y=3x,} \atop {19x=38;}} \right. \\\left \{ {{y=3x,} \atop {x=2;}} \right. \left \{ {{y=3*2,} \atop {x=2;}} \right. \left \{ {{y=6,} \atop {x=2.}} \right.$

ответ: 2; 6.

$b)\\\left \{ {{2x-y=2,} \atop {3x+y=8;}} \right. \\\left \{ {{(2x-y)+(3x+y)=2+8,} \atop {2x-y=2;}} \right. \\\left \{ {{5x=10,} \atop {y=2x-2;}} \right. \\\left \{ {{x=2,} \atop {y=2*2-2;}} \right. \left \{ {{x=2,} \atop {y=2.}} \right.$

ответ: 2; 2.

Уровень "B"

$a)\\\left \{ {{4x-y=9,} \atop {3x+7=-1;}} \right. \\\left \{ {{y=4x-9,} \atop {x=\frac{-1-7}{3};}} \right. \\\left \{ {{y=4x-9,} \atop {x=-\frac{8}{3};}} \right. \\\left \{ {{y=-4*\frac{8}{3}-9,} \atop {x=-\frac{8}{3};}} \right.\left \{ {{y=-\frac{32}{3}-\frac{27}{3},} \atop {x=-\frac{8}{3};}} \right. \left \{ {{y=-\frac{59}{3},} \atop {x=-\frac{8}{3}.}} \right.$

ответ: $-\frac{8}{3};-\frac{59}{3}$.

$b)\\\left \{ {{3x-y=7,\hspace{0.1cm}|*3} \atop {2x+3y=1;}} \right. \\\left \{ {{9x-3y=21,} \atop {2x+3y=1;}} \right. \\\left \{ {{(9x-3y)+(2x+3y)=21+1,} \atop {2x+3y=1;}} \right. \\\left \{ {{11x=22,} \atop {y=\frac{1-2x}{3};}} \right. \\\left \{ {{x=2,} \atop {y=\frac{1-2*2}{3}};} \right. \left \{ {{x=2,} \atop {y=\frac{-3}{3};}} \right. \left \{ {{x=2,} \atop {y=-1.}} \right.$

ответ: 2; -1.

Уровень "С"

$a)\\\left \{ {{2x-y=4,} \atop {3x+7=6;}} \right. \\\left \{ {{y=2x-4,} \atop {x=\frac{6-7}{3};}} \right. \\\left \{ {{y=2(x-2),} \atop {x=-\frac{1}{3};}} \right.\\\left \{ {{y=2(-\frac{1}{3}-2),} \atop {x=-\frac{1}{3};}} \right. \left \{ {{y=-2*2\frac{1}{3},} \atop {x=-\frac{1}{3};}} \right.\left \{ {{y=-2*\frac{7}{3},} \atop {x=-\frac{1}{3};}} \right. \left \{ {{y=-\frac{14}{3},} \atop {x=-\frac{1}{3}.}} \right.$

ответ: $-\frac{1}{3};-\frac{14}{3}$.

$b)\\\left \{ {{5x+3y=-2,} \atop {7x-4y=30;}} \right. \\\left \{ {{(5x+3y)+(7x-4y)=-2+30,} \atop {5x+3y=-2;}} \right. \\\left \{ {{12x-y=28,} \atop {5x+3y=-2;}} \right. \\\left \{ {{y=12x-28,} \atop {5x+3(12x-28)=-2;}} \right. \\\left \{ {{y=12x-28,} \atop {5x+36x-84=-2;}} \right. \\\left \{ {{y=12x-28,} \atop {41x=84-2;}} \right. \\\left \{ {{y=12x-28,} \atop {41x=82;}} \right. \\\left \{ {{y=12x-28,} \atop {x=2;}} \right.$

$\left \{ {{y=12*2-28,} \atop {x=2;}} \right. \left \{ {{y=24-28,} \atop {x=2;}} \right. \left \{ {{y=-4,} \atop {x=2.}} \right.$

ответ: 2; -4.

Пояснение:

Для решения систем неравенств использовался метод сложения уравнений друг с другом и выражение y через x.