Solve the following pair of linear equations by the elimination method and the substitution method:
(i) x+y=5 (1)
2x-3y=4 (2)
Elimination method
Multiplying equation (1) by 2, we get equation (3)
(3)
(2)
Subtracting equation (2) from (3), we get
Putting value of y in (1), we get
Therefore,
and
Substitution method
(1)
(2)
From equation (1), we can say that
Putting this in equation (2), we get
Putting value of y in (1), we get
Therefore,
and
(ii) 3x+4y=10 (1)
2x-2y=2 (2)
Elimination method
Multiplying equation (2) by 2, we get (3)
(3)
(1)
Adding (3) and (1), we get
Putting value of x in (1), we get
Therefore,
and
Substitution method
(1)
(2)
From equation (2), we can say that
(3)
Putting this in equation (1), we get
Putting value of y in (3), we get
Therefore,
and
(iii)
(1)
(2)
Elimination method
Multiplying (1) by 3, we get (3)
(3)
(2)
Subtracting (2) from (3), we get
Putting value of y in (1), we get
Therefore,
and
Substitution Method:
(1)
(2)
From equation (1), we can say that
Putting this in equation (2), we get
Putting value of y in (1), we get
Therefore,
and
(iv)
(1)
(2)
Elimination method
Multiplying equation (2) by 2, we get (3)
(3)
(1)
Adding (3) and (1), we get
Putting value of x in (2), we get
Therefore,
and
Substitution method
(1)
(2)
From equation (2), we can say that
Putting this in equation (1), we get
Putting value of y in (1), we get
Therefore,
and
Sanjeeb says
Nice