График какой функции изображён на рисунке? gr4.png

Варианты ответов:
y=1,5x−2
y=−23x−2
y=−2x−3
y=−3x−2

1)Решение системы уравнений   х₁= -1                 х₂=1

                                                         у₁=0,5               у₂=8

2)Решение системы уравнений  х=4;     у₁= -1;    у₂=1.

Объяснение:

Решить систему уравнений:

1)(5х+3)²=8у

 (3х+5)²=8у

Так как правые части равны, приравниваем и левые:

(5х+3)²=(3х+5)²

Раскрыть скобки:

25х²+30х+9=9х²+30х+25

Перенесём всё в левую часть, приравняем к нулю:

25х²+30х+9-9х²-30х-25=0

Приведём подобные члены:

16х²-16=0

Решим уравнение, вычислим значение х:

16х²=16

х²=1

х₁,₂=±√1

х₁= -1

х₂=1

Вычислим значение у:

8у₁=25х²+30х+9      х₁= -1

8у₁=25*(-1)²+30*(-1)+9

8у₁=25-30+9

8у₁=4

у₁=4/8

у₁=0,5

8у₂=25х²+30х+9      х₂= 1

8у₂=25*1²+30*1+9

8у₂=25+30+9

8у₂=64

у₂=64/8

у₂=8

Решение системы уравнений   х₁= -1                 х₂=1

                                                      у₁=0,5               у₂=8

2)3х²+2у²=50

12х²+8у²=50х

Упростить уравнения, первое разделить на 2, второе на 8:

1,5х²+у²=25

1,5х²+у²=6,25х

Умножить первое уравнение на -1, решить систему методом сложения:

-1,5х²-у²= -25

-1,5х²-у²+1,5х²+у²= -25+6,25х

0= -25+6,25х

-6,25х= -25

х= -25/-6,25

х=4

Теперь подставить значение х в любое из двух уравнений системы и вычислить у:

1,5х²+у²=25

у²=25-1,5х²

у²=25-1,5*4²

у²=25-24

у²=1

у₁,₂=±√1

у₁= -1

у₂=1

Решение системы уравнений  х=4;     у₁= -1;    у₂=1.

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