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
.
Vasudha Dwivedi says
It’s better than having tution classes.. Thanx for the support