Question

Solve the following pair of simultaneous equations.

`2/x + 1/y = 10, 3/x - 2/y = 1`

Answer 1

Given equations:

`2/x + 1/y = 10`     ...(1)

`3/x - 2/y = 1`     ...(2)

Let, `a = 1/x, b = 1/y`

Then the equations will become:

2a + b = 10     ...(1)

3a − 2b = 1     ...(2)

Solving equation (1) for b,

2a + b = 10

b = 10 − 2a

Let’s substitute b = 10 − 2a into equation (2)

3a − 2(10 − 2a) = 1

3a − 20 + 4a = 1

3a + 4a − 20 = 1

7a − 20 = 1

7a = 1 + 20

7a = 21

a = `21/7`

∴ a = 3

Now, putting the value of a = 3 in b = 10 − 2a,

b = 10 − 2(3)

b = 10 − 6

∴ b = 4

Thus, finding x and y from `a = 1/x and b = 1/y,`

`a = 1/x = 3`

`∴ x = 1/3`

`b = 1/y = 4`

`∴ y = 1/4`