Solve using the Addition Method.

5x/6 + y/3 = 4/3

2x/3 - y/2 = 11/6

x = 2

y = - 1

Step-by-step explanation:

5x/6 + y/3 = 4/3

2x/3 - y/2 = 11/6

Multiply the above equation by 6 to express in linear form

6 × (5x/6 + y/3 = 4/3)

5x + 2y = 8 (1)

6 × (2x/3 - y/2 = 11/6)

4x - 3y = 11 (2)

Thus, the equation are:

5x + 2y = 8 (1)

4x - 3y = 11 (2)

Next, multiply equation (1) by 3 and equation (2) by 2. This is illustrated below:

3 × (5x + 2y = 8)

15x + 6y = 24 (3)

2 × (4x - 3y = 11)

8x - 6y = 22 ... (4)

Next, add equation 3 and 4 together. This is illustrated below:

.. 15x + 6y = 24... (3)

+ 8x - 6y = 22 (4)

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23x = 46

Divide both side by 23

x = 46/23

x = 2

Next, substitute the value of x into any of the equation. Here, we shall substitute the value of x into equation (3). This is illustrated below:

15x + 6y = 24... (3)

x = 2

15(2) + 6y = 24

30 + 6y = 24

Collect like terms

6y = 24 - 30

6y = - 6

Divide both side by 6

y = - 6/6

y = - 1

Therefore, the value of x and y is

x = 2

y = - 1