1280. 1) [10(x + y) = 30 + 8x, 9(x - y) = -49-8y; Y 2) (21(x - y) = 48 + 20x, 19(y + x) = 100 + 12y.​

1)

[tex]\displaystyle\bf\\\left \{ {{10(x + y) = 30 + 8x} \atop {9(x - y) = - 49 - 8y }} \right. \\ \displaystyle\bf\\\left \{ {{10x + 10y - 8x = 30} \atop {9x - 9y + 8y = - 49 }} \right. \\ \displaystyle\bf\\\left \{ {{2x + 10y = 30} \atop {9x - y = - 49 }} \right. \\ \displaystyle\bf\\\left \{ {{x = 15 - 5y} \atop {9(15 - 5y) - y = - 49 }} \right. \\ \\ 135 - 45y - y = - 49 \\ - 46y = - 49 - 135 \\ 46y = 184 \\ y = 184 \div 46 \\ y = 4 \\ \\ x = 15 - 5 \times 4 \\ x = 15 - 20 \\ x = - 5[/tex]

Ответ: ( - 5 ; 4 )

2)

[tex]\displaystyle\bf\\\left \{ {{21(x - y) = 48 + 20x} \atop {19(y + x) = 100 + 12y }} \right. \\ \displaystyle\bf\\\left \{ {{21x - 21y - 20x = 48 } \atop {19x + 19y - 12y = 100 }} \right. \\ \displaystyle\bf\\\left \{ {{x - 21y = 48} \atop {19x + 7y = 100 }} \right. \\ \displaystyle\bf\\\left \{ {{x = 21y + 48} \atop {19(21y + 48) +7 y = 100 }} \right. \\ \\ 399y + 912 + 7y = 100 \\ 406y = 100 - 912 \\ 406y = - 812 \\ y = - 812 \div 406 \\ y = - 2 \\ \\ x = 21 \times ( - 2) + 48 \\ x = - 42 + 48 \\ x = 6[/tex]

Ответ: ( 6 ; - 2 )

Пошаговое объяснение:

№1

{10(х + у) = 30 + 8х

{9(х - у) = -49 - 8у

{10х + 10у = 30 + 8х

{9х - 9у = -49 - 8у

{10х + 10у - 8х = 30

{9х - 9у + 8у = -49

{2х + 10у = 30

{9х - у = -49

{2х + 10у = 30

{у = 9х + 49

1)

2х + 10у = 30

2х + 10(9х + 49) = 30

2х + 90х + 490 = 30

92х = 30 - 490

92х = -460

х = -460 : 92

х = -5

2)

у = 9х + 49

у = 9 * (-5) + 49

у = -45 + 49

у = 4

(-5; 4)

№2

{21(х - у) = 48 + 20х

{19(у + х) = 100 + 12у

{21х - 21у = 48 + 20х

{19у + 19х = 100 + 12у

{21х - 21у - 20х = 48

{19у + 19х - 12у = 100

{х - 21у = 48

{19х + 7у = 100

{х = 48 + 21у

{19х + 7у = 100

1)

19х + 7у = 100

19(48 + 21у) + 7у = 100

912 + 399у + 7у = 100

399у + 7у = 100 - 912

406у = -812

у = -812 : 406

у = -2

2)

х = 48 + 21у

х = 48 + 21 * (-2)

х = 48 - 42

х = 6

(6; -2)