**Solve the following pairs of equations by reducing them to a pair of linear equations:**

**(i)** **(1)**

** (2)**

Let and

Putting this in equation **(1)** and **(2)**, we get

and

and

and

and

**(3)** and **(4)**

and

and

We know that and

Putting value of **p** and **q** in this we get

and

**(ii) ** **(1)**

** (2)**

Let and

Putting this in **(1)** and **(2)** we get

**(3)**

**(4)**

Multiplying **(3)** by 2 and subtracting it from** (4)**, we get

Putting value of **q** in **(3)**, we get

Putting values of **p and q** in and , we get

and

and

and

**(iii) ** **(1)**

**(2)**

Let **(3)**

Putting **(3)** in **(1)** and **(2)**, we get

**(4)**

**(5)**

Multiplying **(4)** and 3 and **(5)** by 4, we get

And,

**(6)** **(7)**

Subtracting **(7)** from **(6)**, we get

Putting value of **y **in **(4)**, we get

Putting value of **p** in **(3)**, we get

Therefore, and

**(iv) ** **(1)**

** (2)**

Let and

Putting this in **(1)** and **(2)**, we get

**(3)**

**And**,

** (4)**

Multiplying **(3)** by 3 and adding it to **(4)**, we get

Putting this in **(3)**, we get

Putting values of **p and q** in and , we get

and

and

and

**(v)** ** (1)**

**(2)**

Dividing both the equations by **xy**, we get

**(3)**

**(4)**

Let and

Putting these in **(3)** and **(4)**, we get

**(5)**

** (6)**

From equation **(5)**, we can say that

Putting value of p in **(6)**, we get

Putting value of **q** in **(5)**, we get

Putting value of **p and q** in and , we get

and

**(vi)** ** (1)**

** (2)**

Dividing both the equations by **xy**, we get

**(3)**

**(4)**

Let and

Putting these in **(3)** and **(4)**, we get

** (5)**

**(6)**

From **(5)**, we can say that

Putting this in **(6)**, we get

Putting value of **q** in **(p=2-2q)**, we get

Putting values of **p and q** in ( and ), we get

and

**(vii)** ** (1)**

**(2)**

Let and

Putting this in **(1)** and **(2)**, we get

**(3)**

**(4)**

From equation **(3)**, we can say that

**(5)**

Putting this in **(4)**, we get

Putting value of **p** in **(5)**, we get

Putting values of **p and q** in and ,we get

and

**(6)** and **(7)**

Adding **(6)** and **(7)**, we get

Putting in **(7)**, we get

Therefore, and

**(viii)** ** (1)**

**(2)**

Let and

Putting this in **(1)** and **(2)**, we get

and

** (3)** and **(4)**

Adding** (3)** and **(4)**, we get

Putting value of **p** in **(3)**, we get

Putting value of **p** and **q** in ** and ****,** we get

and

**(5)** and ** (6)**

Adding **(5)** and **(6)**, we get

Putting in **(5)** , we get

Therefore, and .