#### Solve simultaneous linear equations:

(i) 3/x + 4y = 7

5/x + 6y = 13

(ii) 5x – 9 = 1/y

x + 1/y = 3.

**Solution:**

(i) 3/x + 4y = 7 ….. (1)

5/x + 6y = 13 ….. (2)

Substitute 1/x = a in equation (1) and )@)

3a + 4y = 7 …. (3)

5a + 6y = 13 ….. (4)

Multiply equation (3) by 5 and (4) by 3

15a + 20y = 35

15a + 18y = 39

Subtracting both the equations

2y = -4

So we get

y = – 4/2 = – 2

Substitute the value of y in equation (3)

3a + 4 (-2) = 7

By further calculation

3a – 8 = 7

3a = 7 + 8 = 15

So we get

3a = 15

a = 15/3 = 5

Here x = 1/a = 1/5

Therefore, x = 1/5 and y = – 2.

(ii) 5x – 9 = 1/y ….. (1)

x + 1/y = 3 ….. (2)

Substitute 1/y = b in (1) and (2)

5x – 9 = b

5x – b = 9 ….. (3)

x + b = 3 ….. (4)

By adding equation (3) and (4)

5x – b = 9 ….. (3)

x + b = 3 ….. (4)

So we get

6x = 12

By division

x = 12/6 = 2

Substitute the value of x in equation (4)

2 + b = 3

b = 3 – 2

b = 1

Here 1/y = 1

b = 1/y

y = 1

Therefore, x = 2 and y = 1.

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