(ii) 3x + 4y - 10 = 0 and 2x – 2y -2 = 0
Soln.
Elimination method
Substituting x = 2 in (i)
Solution is x = 2, y = 1
3x
+
4y
=
10
2x
–
2y
=
2
Multiplying (ii) by 2, we get
Adding (i) and (iii)
3x
+
4y
=
10
4x
–
4y
=
4
7x
=
14
x
=
2
... (i)
... (ii)
... (iii)
3(2)
+
4y
=
10
4y
=
10
–
6
4y
=
4
y
=
1
4x – 4y = 4
3x
+
4y
=
10
... (i)
7x
=
14
x
=
14
7
6
+
4y
=
10
y
=
4
4
2
Are the coefficients of X same ?
NO !!
Are the coefficients of Y same ?
NO !!
First in this sum will have to either make the coefficient of the X same or Y same
To make the coefficient of X same we will have to multiplying equation (i) by 2 and eqn (ii) by 3
To make the coefficient of Y same we will have to multiplying equation (ii) by 2
OR
In elimination method, keep variable on L.H.S and constant on R.H.S
Check the coefficient of the variables
Number the equation as equation (iii)
How to get the value of ‘y’ ?
Either equation (i),(ii) or equation (iii)
We have to substitute x = 2
We need to either remove x or remove y
Which variable can be removed ?
Whichever variable’s coefficient is same
Here coefficent of
y is same
To remove y, we need to add
As Signs are different
Q. Solve the following pair of linear equations by the elimination method
(and the substitution method)