Question

Решить систему 2(х-у)=х-6 5(х-у)=2(х-у)+10

Answer 1

2(х-у)=х-6,
5(х-у)=2(х-у)+10,

2х-2у=х-6,
5х-5у=2х-2у+10,

2х-х=2у+6,
5х-5у-2х+2у=10,

х=2у+6,
3х-3у=10,

3*(2у+6)-3у=10,
6у+18-3у=10,
3у=10-18,
3у=-8,
у = - 2 2/3,
х = (-2 2/3*2)+6 = -16/3+6 = -16/3+18/3 = 2/3,

ответ:  (2/3; -2 2/3)

Answer 2

To solve the system of equations:

1. 2(x - y) = x - 6
2. 5(x - y) = 2(x - y) + 10

We can start by simplifying and then solving for one of the variables.

Step 1: Simplify the equations.

1. 2x - 2y = x - 6 (Distribute the 2 on the left side)
2. 5x - 5y = 2x - 2y + 10 (Distribute the 5 on the left side)

Step 2: Combine like terms.

1. 2x - 2y = x - 6 (No change)
2. 5x - 5y = 2x - 2y + 10 (Combine 2x and -2x on the right side)

2x - 2y is common to both equations, so let's simplify further.

Step 3: Isolate the common term.

1. 2x - 2y = x - 6 (No change)
2. 5x - 5y - 2x + 2y = 10 (Subtract 2x - 2y from both sides of the second equation)

Now, simplify the second equation.

3x - 3y = 10

Step 4: Solve for one variable.

From the first equation, we can isolate x:

2x - 2y = x - 6

Add 6 to both sides:

2x - 2y + 6 = x

Subtract x from both sides:

2x - x - 2y + 6 = 0

Simplify:

x - 2y + 6 = 0

Subtract 6 from both sides:

x - 2y = -6

Step 5: Substitute the value of x in terms of y into the second equation.

3x - 3y = 10

Substitute x - 2y = -6:

3(-6) - 3y = 10

Simplify:

-18 - 3y = 10

Step 6: Solve for y.

Add 18 to both sides:

-3y = 28

Now, divide by -3:

y = -28 / -3

y ≈ 9.3333 (rounded to four decimal places)

Step 7: Find the value of x.

We already have the expression for x:

x - 2y = -6

Substitute the value of y:

x - 2(9.3333) = -6

x - 18.6666 = -6

Add 18.6666 to both sides:

x = -6 + 18.6666

x ≈ 12.6666 (rounded to four decimal places)

So, the solution to the system of equations is approximately:

x ≈ 12.6666 y ≈ 9.3333