Question

решите задания с первого по четвёртое как можно быстрее, я на уроке стараюсь тянуть время и получается это у меня ой как плохо

Answer 1

1.

$\left \{ {{5x+3y=4} \atop {2x-y=-5}} \right. \left \{ {{5x+3y=4} \atop {-y=-5-2x}} \right. \left \{ {{5x+3y=4} \atop {y=5+2x}} \right. \left \{ {{5x+3\cdot(5+2x)=4} \atop {y=5+2x}} \right. \left \{ {{5x+15+6x=4} \atop {y=5+2x}} \right. \left \{ {{11x=4-15} \atop {y=5+2x}} \right. \left \{ {{11x=-11} \atop {y=5+2x}} \right. \\ \\ \left \{ {{x=-\frac{11}{11}} \atop {y=5+2x}} \right. \left \{ {{x=-1} \atop {y=5+2\cdot(-1)}} \right. \left \{ {{x=-1} \atop {y=5-2}} \right. \left \{ {{x=-1} \atop {y=3}} \right$

2. Пусть

х - менеджеров получили по 10000 рублей

у - менеджеров получили по 15000 рублей

Тогда

$\left \{ {{x+y=30} \atop {10000x+15000y=390000}} \right. \left \{ {{x+y=30} \atop {10x+15y=390}} \right. \left \{ {{y=30-x} \atop {10x+15\cdot (30-x)=390}} \right. \left \{ {{y=30-x} \atop {10x+450-15x=390}} \right. \left \{ {{y=30-x} \atop {-5x=390-450}} \right.$$\left \{ {{y=30-x} \atop {-5x=-60}} \right. \left \{ {{y=30-x} \atop {5x=60}} \right. \left \{ {{y=30-x} \atop {x=\frac{60}{5}}} \right. \left \{ {{y=30-12} \atop {x=12}} \right. \left \{ {{y=18} \atop {x=12}} \right.$

12 менеджеров получили по 10000 рублей

18 менеджеров получили по 15000 рублей

3.

$\left \{ {{10-4\cdot(2x+5)=6y-13} \atop {4y-63=5\cdot (4x-2y)+2}} \right. \left \{ {{10-8x-20=6y-13} \atop {4y-63=20x-10y+2}} \right. \left \{ {{-8x-10=6y-13} \atop {4y+10y=20x+63+2}} \right. \left \{ {{-8x-6y=-13+10} \atop {14y-20x=65}} \right. \\ \\ \left \{ {{-8x-6y=-3} \atop {14y-20x=65}} \right. \left \{ {{8x+6y=3} \atop {14y-20x=65}} \right. \left \{ +{{30y+40x=15} \atop {28y-40x=130}} \right. \ \ \ \ 58y=145; \ \ \ y =\frac{145}{58}=\frac{5}{2}$

$8x+6y=3; \\ \\ 8x+6\cdot\frac{5}{2}=3 \\ \\ 8x+3\cdot 5 =3; \\ \\ 8x+15=3; \\ \\ 8x=3-15; \\ \\ 8x=-12; \\ \\ x=-\frac{12}{8}=-\frac{3}{2}$

4.

$y=kx+b; \\ \\ \left \{ {{26=k\cdot (-3)+b} \atop {-22=k\cdot 5+b}} \right. \left \{ {{26=-3k+b} \atop {-22=5k+b}} \right. \left \{ {{b=26+3k} \atop {-22=5k+26+3k}} \right. \left \{ {{b=26+3k} \atop {-22-26=8k}} \right. \left \{ {{b=26+3k} \atop {-48=8k}} \right. \left \{ {{b=26+3k} \atop {k=-\frac{48}{8}}} \right. \left \{ {{b=26+3\cdot(-6)} \atop {k=-6} \right. \\ \\ \left \{ {{b=26-18} \atop {k=-6} \right. \left \{ {{b=8} \atop {k=-6} \right.$

$y=-6x+8$