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## 28 April, 2009

### Solving pair of linear equations by substitution method

Solve for x and y by substitution method

General Method:

Consider the general equations a1x +b1y = c1 and a2x +b2y = c2.
Take either of the two equations and express one of the variable say (x) in terms of the other i.e. y.
Now, sustitute (put) the value of x (in terms of y) obtained in the second equations.
The second equation will become a linear equation in one variable i.e. y . Solve it and find y.
Now, put the value of y in the equation obtained in step 2, to get the value of x.

Example 1

2x + 4y =1 --- (1)
3x + 5y =2 --- (2)
From (1) 2x = 1- 4y
x = (1-4y)/2 ----- (3)
Now put (3) in (1)
2 (1-4y)/2 + 5y = 2
1 - 4y+ 5y = 2
1+y = 2
y=1
Now put (y = 1) in (3)
x = -3/2
y = 1

Example 2

x + 2y = 3 ------ i
2x + 4y = 6 ------ ii
From i,
x = 3 – 2y ------ iii
Now put iii in ii,
2(3 – 2y) + 4y = 6
6 - 4y + 4y = 6
6 = 6
This is always true.
So there are infinitely many solutions.

Example 3
4x + 6y = 7----- i
8x + 12y = 9 ----- ii
From i,
4x = 7 – 6y ------ iii
x = (7 – 6y)/4
Now put iii in ii,
8((7 – 6y)/4) + 12y = 9
14 – 12y +12y = 9
14 = 9
which is a false statement.
So there is no solution.

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