Verified answer

1) Ответ: x=2,5 ; y=1

[tex]\left \{ {{5(2x - 3y) = 4x} \atop {6x - 4y = 4(2x - 1) - 5}} \right. \\ \\ \left \{ {{10x - 15y = 4x} \atop {6x - 4y = 8x - 4 - 5}} \right. \\ \\ \left \{ {{10x - 15y - 4x = 0} \atop {6x - 4y - 8x = - 4 - 5}} \right. \\ \\ \left \{ {{6x - 15y = 0 \: \: \: \: \: \: \: \: \: \: \: \: \: } \atop { - 2x - 4y = - 9 \: \:| \times 3}} \right. \\ \\ [/tex]

[tex]\left \{ {{6x - 15y = 0} \atop { - 6x - 12y = - 27}} \right. + \\ - 27y = - 27 \\ y = 1[/tex]

И вместо у поставим 1

[tex] - 2x - 4y = - 9 \\ - 2x - 4 \times 1 = - 9 \\ - 2x - 4 = - 9 \\ - 2x = - 5 \\ x = 2.5[/tex]

2)

[tex]\left \{ {{ \frac{3}{7}(x - 2) + \frac{2}{7} (x + y) = 4} \atop {3(x - 2) + 5(x + y) = 7}} \right. \\ \\ \left \{ {{3(x - 2) + 2(x + y) = 28} \atop {3(x - 2) + 5(x + y) = 7}} \right. \\ \\ \left \{ {{3x - 6 + 2x + 2y = 28} \atop {3x - 6 + 5x + 5y = 7}} \right. \\ \\ \left \{ {{5x + 2y = 34 \: \:| \times ( - 5) } \atop {8x + 5y = 13 \: \:| \times 2 }} \right. \\ \\[/tex]

[tex]\left \{ {{ - 25x - 10y = - 170} \atop {16x + 10y = 26}} \right. + \\ 9x = - 144 \\ x = - 16[/tex]

И вместо х поставим -16

5x+2y=34

5•(-16)+2y=34

-80+2y=34

2y=114

y=57

Объяснение:

№1

5(2х - 3у) = 4х

6х - 4у = 4(2х - 1) - 5

10х - 15у = 4х

6х - 4у = 8х - 4 - 5

10х - 15у - 4х = 0

6х - 4у - 8х = -4 - 5

6х - 15у = 0

-2х - 4у = -9 | : -2

6х - 15у = 0

х + 2у = 4,5

6х - 15у = 0

х = 4,5 - 2у

1)

6х - 15у = 0

6(4,5 - 2у) - 15у = 0

27 - 12у - 15у = 0

-12у - 15у = 0 - 27

-27у = -27

у = -27 : (-27)

у = 1

2)

х = 4,5 - 2у

х = 4,5 - 2*1

х = 4,5 - 2

х = 2,5

Ответ: (2,5; 1)

№2

3/7(х - 2) + 2/7(х + у) = 4

3(х - 2) + 5(х + у) = 7

3/7х - 6/7 + 2/7х + 2/7у = 4 | * 7

3х - 6 + 5х + 5у = 7

3х - 6 + 2х + 2у = 28

8х + 5у = 7 + 6

5х + 2у = 28 + 6

8х + 5у = 13

5х + 2у = 34 | : 2

8х + 5у = 13

2,5х + у = 17

8х + 5у = 13

у = 17 - 2,5х

8х + 5у = 13

1)

8х + 5у = 13

8х + 5(17 - 2,5х) = 13

8х + 85 - 12,5х = 13

8х - 12,5х = 13 - 85

-4,5х = -72

х = -72 : (-4,5)

х = 16

2)

у = 17 - 2,5х

у = 17 - 2,5*16

у = 17 - 40

у = -23

Ответ: (16; -23)