#### Solve simultaneous linear equations:

(i) 2/x + 2/3y = 1/6

2/x – 1/y = 1

(ii) 3/2x + 2/3y = 5

5/x – 3/y = 1.

**Solution:**

(i) 2/x + 2/3y = 1/6 ….. (1)

2/x – 1/y = 1 ….. (2)

By subtracting both the equations

5/3y = -5/6

By cross multiplication

– 15y = 30

By division

y = 30/ -15 = – 2

Substitute the value of y in equation (1)

2/x + 2/ (3 × (-2)) = 1/6

By further calculation

2/x – 1/3 = 1/6

So we get

2/x = 1/6 + 1/3

Taking LCM

2/x = (1 + 2)/ 6 = 3/6

By cross multiplication

x = (2 × 6)/3 = 12/3 = 4

Therefore, x = 4 and y = – 2.

(ii) 3/2x + 2/3y = 5 ….. (1)

5/x – 3/y = 1 ….. (2)

Multiply equation (1) by 1 and (2) by 2/9

3/2x + 2/3y = 5

10/9x – 2/3y = 2/9

By adding both the equations

(3/2 + 10/9)1/x = 5 + 2/9

Taking LCM

(27 + 20)/ 18 × 1/x = (45 + 2)/ 9

By further calculation

47/18x = 47/9

By cross multiplication

x = (47 × 9)/ (47 × 18) = ½

Substitute the value of x in equation (2)

5/ ½ – 3/y = 1

By further calculation

10 – 3/y = 1

3/y = 10 – 1 = 9

So we get

y = 3/9 = 1/3

Therefore, x = ½ and y = 1/3.

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