Question

6 = 3(Х + У) 6 – 5(Х – У) = 8 Х – 2 У

Answer 1

Объяснение:

3х+3у=6

6-5х+5у=8х-2у

3х+3у=6

-5х-8х+5у+2у=-6

3х+3у=6 |•(-7)

-13х+7у=-6 |•3

-21х-21у=-42

-39х+21у=-18

-60х=-60

х=1

у=1

Answer 2

To solve the system of equations:

1. 6 = 3(Х + У)
2. 6 - 5(Х - У) = 8Х - 2У

We can start by solving equation 1 for one of the variables (let's solve for Х):

1. 6 = 3(Х + У)

Divide both sides by 3:

(6 / 3) = (3(Х + У) / 3)

2 = Х + У

Now, let's substitute this expression for Х in equation 2:

2. 6 - 5(Х - У) = 8Х - 2У

3. 6 - 5(2 - У) = 8(2 - У) - 2У

Now, distribute the -5 and 8 on the right side of the equation:

6 - 10 + 5У = 16 - 8У - 2У

Combine like terms:

-4 + 5У = 16 - 10У

Now, move the terms involving У to one side of the equation and the constant terms to the other side:

5У + 10У = 16 + 4

15У = 20

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

У = 20 / 15 У = 4/3

Now that you have the value of У, you can substitute it back into equation 2 to find the value of Х:

2 = Х + (4/3)

Subtract (4/3) from both sides to isolate Х:

2 - (4/3) = Х

To make 2 a fraction with a common denominator of 3:

(6/3) - (4/3) = Х

(6 - 4) / 3 = Х

2/3 = Х

So, the solution to the system of equations is:

Х = 2/3 У = 4/3