Question

5(3x - 2)+2=-2(4y+1),3(y-x)+ 8 = 3x -(5x - y).​

Answer 1

Ответ:

5(3x - 2)+2=-2(4y+1),

3(y-x)+ 8 = 3x -(5x - y)

15x-10+2=-8y-2

3y-3x+8=3x-5x+y

15x+8y=-2+10-2

3y-3x-3x+5x-y=-8

15x+8y=6

2y-x=-8

15x+8y=6

-x=-8-2y

-15x-8y=-6

x=8+2y

-15(8+2y)-8y=-6

-120-30y-8y=-6

-30y-8y=-6+120

-38y=114

y=114÷-38

y=-3

x=8+2×-3

x=2

ответ:

(x;y)=(2;-3)

Answer 2

To solve this system of linear equations:

1. 5(3x - 2) + 2 = -2(4y + 1)
2. 3(y - x) + 8 = 3x - (5x - y)

Let's start by simplifying each equation:

Equation 1: 5(3x - 2) + 2 = -2(4y + 1)

Distribute on both sides:

15x - 10 + 2 = -8y - 2

Combine like terms:

15x - 8 = -8y - 2

Equation 2: 3(y - x) + 8 = 3x - (5x - y)

Distribute on both sides:

3y - 3x + 8 = 3x - 5x + y

Combine like terms:

3y - 3x + 8 = -2x + y

Now, we have a system of two equations:

1. 15x - 8 = -8y - 2
2. 3y - 3x + 8 = -2x + y

We can solve this system of equations by either substitution or elimination. Let's use the elimination method.

First, let's make the coefficients of y in both equations equal by multiplying the second equation by 8 (so that both coefficients of y become -8):

1. 15x - 8 = -8y - 2
2. 24y - 24x + 64 = -16x + 8y

Now, we have:

1. 15x - 8 = -8y - 2
2. 24y - 24x + 64 = -16x + 8y

Now, we can add both equations to eliminate the variable y:

(15x - 8) + (24y - 24x + 64) = (-8y - 2) + (-16x + 8y)

Simplify and combine like terms:

15x - 8 + 24y - 24x + 64 = -8y - 2 - 16x + 8y

Now, let's collect like terms:

(-8x + 24y + 56) = (-8x + 6y - 2)

Now, let's isolate the variables on one side and constants on the other side:

-8x + 8x + 24y - 6y = -2 - 56

18y - 6y = -58

12y = -58

Now, divide both sides by 12 to solve for y:

y = (-58) / 12 y = -29/6

Now that we have found the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use Equation 1:

15x - 8 = -8(-29/6) - 2

15x - 8 = 116/3 - 2

15x - 8 = (116/3) - (6/3)

15x - 8 = (116 - 6) / 3

15x - 8 = 110/3

Now, isolate x:

15x = 110/3 + 8

15x = (110 + 24) / 3

15x = 134/3

Now, divide both sides by 15 to solve for x:

x = (134/3) / 15

x = (134/3) * (1/15)

x = 134/45

So, the solution to the system of equations is:

x = 134/45 y = -29/6