4-5-6-7-8 giải giúp mình gấp gấp

`bb\color{Red}\text{Giải:}`

`4.` `{(3x - 9y = 2 \text{ (1)}), (- 2x + 5y = 1 \text{ (2)}):}`

`@`Từ `(1)` ta có: `3x - 9y = 2 `

`3(x−3y)=2 `

`x−3y=2/3`

`x=2/3+3y`

`@`Thay `x=2/3+3y` vào `(2)` ta được: `- 2(2/3+3y) + 5y = 1`

`-4/3-y=1`

`-y=1+4/3`

`-y=7/3`

`y=-7/3`

`@`Thay `y=-7/3` vào `x=2/3+3y` ta được: `x=2/3+3(-7/3)`

`x=-19/3`

`bb{Vậy::}` Hpt có nghiệm`(-19/3;-7/3)`.

`5.` `{(-3x - 5y = -35 \text{ (1)}), (6x - 10y = -10 \text{ (2)}):}`

`@`Từ `(1)` ta có: `-3x - 5y = -35`

`3x + 5y = 35` 

`@`Chia phương trình `(2)` cho 2, ta được:

`3x - 5y = -5` 

`@`Cộng phương trình `3x + 5y = 35` và `3x - 5y = -5` ta có:

`6x = 30`

`x = 5`

`@` Thay `x = 5` vào `3x + 5y = 35` ta được: `3(5) + 5y = 35`

`15 + 5y = 35`

`5y = 20`

`y = 4`

`bb{Vậy::}` Hpt có nghiệm `(5; 4)`.

`6.` `{(7x - 4y = 8 \text{ (1)}), (-2x - 4y = -12 \text{ (2)}):}`

`@`Từ `(2)` ta có: `-2x - 4y = -12`

`2x + 4y = 12`

`x + 2y = 6` 

`x = 6-2y` 

`@`Thay `x = 6 - 2y` vào `(1)`: `7(6 - 2y) - 4y = 8`

`42 - 14y - 4y = 8`

`42 - 18y = 8` `-18y = -34`

`y = 34 / 18`

`y= 17 / 9`

`@`Thay `y = 17 / 9` vào `x = 6 - 2y`: `x = 6 - 2(17 / 9)`

`x = 20 / 9`

`bb{Vậy::}` Hpt có nghiệm `(20 / 9; 17 / 9)`.

`7.` `{(8x - 6y = 6 \text{ (1)}), (-3x + 4y = 3 \text{ (2)}):}`

`@`Từ `(2)` ta có: `-3x + 4y = 3`

`3x = 4y - 3`

`x = (4y - 3) / 3`

`@`Thay `x = (4y - 3) / 3` vào `(1)` ta được:

`8((4y - 3) / 3) - 6y = 6`

`8(4y−3)−18y=18`

`32y−24−18y=18`

`14y=42` `y=3`

`@`Thay `y = 3` vào `x=(4y - 3) / 3` ta được: `x=(4*3-3)/3`

`x = 3`

`bb{Vậy::}` Hpt có nghiệm `(3; 3)`.

`8.` `{(4x - 5y = 35 \text{ (1)}), (-6x + y = -28 \text{ (2)}):}`

`@`Từ `(2)` ta có: `-6x+y=-28`

`y=-28+6x`

`@`Thay `y = -28+6x` vào `(1)` ta được: `4x - 5(-28+6x) = 35`

`4x−30x+140=35 `

`−26x=−105 `

`x=105/26`

`@`Thay `x=105/26` vào `y = -28+6x` ta được: `y = -28+6(105/26)`

`y=-49/13`

`bb{Vậy::}` Hpt có nghiệm `(105/26; -49/13)`.

Let's solve these systems of linear equations one by one:

**1.** \( -3x - 5y = -35 \)  
\( 6x - 10y = -10 \)

First, simplify the second equation by dividing through by 2:  
\( 3x - 5y = -5 \)

Now, add this to the first equation:  
\[
-3x - 5y + (3x - 5y) = -35 - 5
\]
\[
-10y = -40
\]
\[
y = 4
\]

Substitute \( y = 4 \) into \( 3x - 5y = -5 \):  
\[
3x - 5(4) = -5
\]
\[
3x - 20 = -5
\]
\[
3x = 15
\]
\[
x = 5
\]

So the solution is \( (x, y) = (5, 4) \).

---

**2.** \( 7x - 4y = 8 \)  
\( -2x - 4y = -12 \)

Add the equations to eliminate \( y \):  
\[
7x - 4y + (-2x - 4y) = 8 - 12
\]
\[
5x - 8y = -4
\]

Rearrange and solve for \( x \) and \( y \):  
\[
7x - 4y = 8
\]
\[
-2x - 4y = -12
\]

Subtract the second from the first equation:  
\[
(7x - 4y) - (-2x - 4y) = 8 - (-12)
\]
\[
9x = 20
\]
\[
x = \frac{20}{9}
\]

Substitute \( x = \frac{20}{9} \) into \( 7x - 4y = 8 \):  
\[
7 \left(\frac{20}{9}\right) - 4y = 8
\]
\[
\frac{140}{9} - 4y = 8
\]
\[
-4y = 8 - \frac{140}{9}
\]
\[
-4y = \frac{72 - 140}{9}
\]
\[
-4y = \frac{-68}{9}
\]
\[
y = \frac{17}{9}
\]

So the solution is \( \left(x, y\right) = \left(\frac{20}{9}, \frac{17}{9}\right) \).

---

**3.** \( 8x - 6y = 6 \)  
\( -3x + 4y = 3 \)

Multiply the first equation by 2 and the second by 3 to align coefficients:  
\[
16x - 12y = 12
\]
\[
-9x + 12y = 9
\]

Add these equations:  
\[
16x - 12y + (-9x + 12y) = 12 + 9
\]
\[
7x = 21
\]
\[
x = 3
\]

Substitute \( x = 3 \) into \( 8x - 6y = 6 \):  
\[
8(3) - 6y = 6
\]
\[
24 - 6y = 6
\]
\[
-6y = -18
\]
\[
y = 3
\]

So the solution is \( (x, y) = (3, 3) \).

---

**4.** \( 4x - 5y = 35 \)  
\( -6x + y = -28 \)

Solve the second equation for \( y \):  
\[
y = 6x - 28
\]

Substitute \( y = 6x - 28 \) into \( 4x - 5y = 35 \):  
\[
4x - 5(6x - 28) = 35
\]
\[
4x - 30x + 140 = 35
\]
\[
-26x + 140 = 35
\]
\[
-26x = -105
\]
\[
x = \frac{105}{26}
\]

Substitute \( x = \frac{105}{26} \) into \( y = 6x - 28 \):  
\[
y = 6 \left(\frac{105}{26}\right) - 28
\]
\[
y = \frac{630}{26} - 28
\]
\[
y = \frac{630 - 728}{26}
\]
\[
y = \frac{-98}{26}
\]
\[
y = -\frac{49}{13}
\]

So the solution is \( \left(x, y\right) = \left(\frac{105}{26}, -\frac{49}{13}\right) \).