#### Solve the linear equations:

(i) 2x – 3y/4 = 3

5x – 2y – 7 = 0

(ii) 2x + 3y = 23

5x – 20 = 8y

**Solution:**

(i) 2x – 3y/4 = 3

5x – 2y – 7 = 0

We can write it as

2x/1 – 3y/4 = 3

By taking LCM

(8x – 3y)/ 4 = 3

By cross multiplication

8x – 3y = 12 ….. (1)

5x – 2y = 7 …. (2)

Now multiply equation (1) by 2 and (2) by 3

16x – 6y = 24

15x – 6y = 21

By subtracting both the equations

x = 3

Now substituting the value of x in equation (1)

8 × 3 – 3y = 12

By further calculation

24 – 3y = 12

– 3y = 12 – 24

So we get

– 3y = – 12

y = – 12/-3 = 4

Therefore, x = 3 and y = 4.

(ii) 2x + 3y = 23

5x – 20 = 8y

We can write it as

2x + 3y = 23 …. (1)

5x – 8y = 20 …. (2)

By multiplying equation (1) by 5 and equation (2) by 2

10x + 15y = 115

10x – 16y = 40

By subtracting both the equations

31y = 75

So we get

y = 75/31 = 2 13/31

By substituting the value of y in equation (1)

2x + 3 (75/31) = 23

By further calculation

2x + 225/31 = 23

We can write it as

2x = 23/1 – 225/31

Taking LCM

2x = (713 – 225)/ 31 = 488/31

So we get

x = 488/ (31 × 2) = 244/ 31 = 7 27/31

Therefore, x = 7 27/31 and y = 2 13/31.

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