Решите систему уравнений: {5x-2y=0 {2x-5y=-21 {2-4y=3 (x-2) {2(x+y)=5y+2,5

Question

Решите систему уравнений: {5x-2y=0 {2x-5y=-21 {2-4y=3 (x-2) {2(x+y)=5y+2,5

Answer 1

5х - 2y = 0

2x - 5y = 21

x = 0.4y

0.8y - 5y = 21

x = 0.4y

-4,2y = 21

y= -5

x = -5 •0.4 = -2

2-4y=3 (x-2)

2(x+y)=5y+2,5

2 - 4y = 3x - 6

2x + 2y = 5y + 2,5

3x + 4y = 8

2x - 3y = 2,5

y = (8-3x) / 4

2x - 12 - 2,25x = 2,5

y = (8-3x) / 4

-0.25x = 14,5

x = - 58

y = (8 - 174)/4 = -41,4

Answer 2

1 система

{5x-2y=0 |×(-2)

{2x-5y=-21 |×5

{-10х + 4у= 0

{10х - 25у= -105

-10х + 4у + 10х - 25у= 0 - 105

4у - 25у= -105

-21у= -105 | ×(-1)

21у= 105

у= 5

5х - 2у= 0

5х - 2×5= 0

5х= 10

х= 2

Ответ: (2; 5).

2 система

{2-4y=3 (x-2)

{2(x+y)=5y+2,5

{2 - 4у= 3х - 6

{2х + 2у= 5у + 2.5

{-4у - 3х= -6 - 2

{2х + 2у - 5у= 2.5

{-4у - 3х= -8 |×(-3)

{2х - 3у= 2.5 |×4

{12у + 9х= 24

{8х - 12у= 10

12у + 9х + 8х - 12у= 24 + 10

9х + 8х= 34

17х= 34

х= 2

-4у - 3х= -8

-4у - 3×2= -8

-4у= -8 + 6

-4у= -2 |×(-1)

4у= 2

у= 0.5

Ответ: (2; 0.5).