# Which of the following systems is equivalent to the given system? 2/3x - y = 2, x +1/2y = -3

2x - 3y = 6 and 2x + y = 6

6x - 3y = 6 and 2x + y = 10

2x - 3y = 6 and 2x + y = -6

**Solution: **

Given: System of equations are 2/3x - y = 2 and x +1/2y = -3

We have to check which of the given system of equations is equivalent to the given system of equations

Checking the first set of equations

**1. 2x - 3y = 6 and 2x + y = 6**

First equation ⇒ 2x - 3y = 6

Divide the equation by 3

⇒ 2x/3 - 3y/3 = 6/3

⇒ \(\dfrac{2}{3}\)x - y = 2

The first equation is equivalent to the set

Now check the second equation

2x + y = 6

Divide the equation by 2

⇒ 2x/2 + y/2 = 6/2

⇒ x + ½y = 3

The second equation is not equivalent to the set

Therefore, the first set of the equation is not equivalent to the set of equations.

Checking the second set of equations

**2. 6x - 3y = 6 and 2x + y = 10**

First equation ⇒ 6x - 3y = 6

Divide the equation by 3

⇒ 6/3x - 3/3y = 6/3

⇒ 2x - y = 2

The first equation is not equivalent to the set

Therefore, no need to check the second set.

Checking the third set of equations

**3. 2x - 3y = 6 and 2x + y = -6**

First equation ⇒ 2x - 3y = 6

Divide the equation by 3

⇒ 2/3x - 3/3y = 6/3

⇒ 2/3x - y = 2

The first equation is equivalent to the set

Now check the second equation

⇒ 2x + y = -6

Divide the equation by 2

⇒ 2/2x + 1/2y = -6/2

⇒ x + ½y = -3

The second equation is also equivalent to the set

## Which of the following systems is equivalent to the given system? 2/3x - y = 2, x +1/2 y = -3

**Summary: **

The following set of equations 2x - 3y = 6 and 2x + y = -6 is equivalent to the given set of equations 2/3x - y = 2, x +1/2 y = -3.

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