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

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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.