(iii)
3x
-
y
= 3 ;
9x
-
3y
= 9
Soln.
y + 3
3
x =
9x
-
3y
= 9
... (ii)
... (iii)
Substituting equation (iii) in equation (ii) ;
y + 3
3
9
-
3y
= 9
-
3y
= 9
3y
= 9
9
Since both the variables get cancelled on solving.
These equations do not have a unique solution
3x
-
y
= 3
... (i)
Write their equation either x = something
or
y = something
3
First let us number the equations
+ 9
Consider one of the two equations
Let us Consider equation no. (i)
Consider (i)
Which equation is to be considered
You can consider either of the two equations
It is better to consider simpler of the two equations
3x
-
y
= 3
Number the equation as (iii)
What is the name of the method ?
SUBSTITUTION Method
So we need to substitute something
substitute what ?
Substitute eqn. (iii)
Where ?
In the equation which was not considered
HOMEWORK
2x
+
3y
=
0
;
3x
-
8y
=
0
(v)
Soln.
2x
+
3y
=
0
…(i)
3x
-
8y
=
0
…(ii)
∴
2x
=
-
3y
2
…(iii)
3y
∴
x
=
-
Substituting
x
=
3y
2
-
In eqn
(ii)
∴
3
3y
2
-
-
8y
=
0
∴
-
3y
-
4y
2
=
0
∴
-
7y
=
0
×
2
∴
7y
=
0
-
∴
=
0
y
-7
=
0
y
∴
Substituting
y
=
0
In eqn
…(iii)
-
×
0
3
=
x
2
=
x
0
2
=
x
0
∴
×
2
8y
=
×
2
8 y
=
16 y
=
4
y
Solution is x = 0 , y = 0
First let us number the equations
Write their eqn.
either x = something
or y = something
How to get the value of x ?
We have to substitute
y = 0
Either eqn (i), eqn (ii) or eqn (iii)
Let us substitute eqn (iii)
Consider one of the two equations
Let us Consider equation no. (i)
Consider (i)
Which equation is to be considered
You can consider either of the two equations
It is better to consider simpler of the two equations
2x
+
3y
=
0
What is the name of the method ?
SUBSTITUTION Method
So we need to substitute something
substitute what ?
Substitute eqn. (iii)
Where ?
In the equation which was not considered
Number the equation as (iii)