SUBSTITUTION METHOD SOLVING SIMULTANEOUS LINEAR EQUATIONS -
Suppose we are given two linear equations in x & y
Step.1) Express y in terms of x from one of the given equations.
Step.2) Substitute this value of y in the other equation to obtain a linear equations in x, solve it for x.
Step.3) Substitute the value of x in the relation taken in step.1 and obtain the value of y, we may interchange the role of x & y in the above method.
Example.1) Solve => 4x – 5y = 12 , 5x + y = 15
Ans.) The given equations are => 4x – 5y = 10 …………………… (i)
5x + y = 15 ………………….(ii)
From (ii) we get => 5x + y = 15
y = 15 – 5x ………….(iii)
Substituting y obtained from (iii) in (i)
4x – 5y = 10
=> 4x – 5 (15 – 5x) = 12
=> 4x – 75 + 25x = 12
=> 29x = 75 + 12 = 87
=> x = 3
Now, we will substitute the value x, which is x = 3 in (iii)
=> y = 15 – 5x = 15 – (5 X 3)
=> y = 15 – 15 = 0
Hence x = 3, and y = 0 are the solution of the given equations. (Ans.)
Example.2) Solve => 3x + 2y = 10, 5x – y = 15
Ans.) The given equations are => 3x + 2y = 10 …………………… (i)
5x + y = - 5 ………………….(ii)
From (i), we get –
=> 3x + 2y = 10
(10 – 2y)
=> x = ------------- ……………….(iii)
3
Now we will substitute x in (ii)
=> 5x – y = -5
=> 5x = y – 5
5 (10 – 2y)
=> -------------- = y – 5
3
=> 50 – 10y = 3y – 15
=> 50 + 15 = 10y + 3y
=> 13y = 65
=> y = 5
Now we will substitute y in (iii), and we get
Hence x = 0, and y = 5 are the solution of the given equations.
(10 – 2y)
=> x = ------------
3
=> 3x = 10 – 2y = 10 – (2 X 5)
=> x = 0
Hence, x = 0, and y = 5 are the solution of the given equations. (Ans.)