Solving Linear Equations in Two Variables Using Elimination Method :
In this section, we will see some example problems using the concept elimination method.
General form of linear equation in two variables is ax + by + c = 0
Procedure for elimination method :
The flow chart given below will help us to understand the procedure better.
Question 1 :
Solve the following system of linear equations by elimination method
13x + 11y = 70 , 11x + 13y = 74
Solution :
13x + 11y = 70 -------- (1)
11x + 13y = 74 -------- (2)
By considering the given equations,
Coefficient of x in (1) = Coefficient of y in (2)
Coefficient of y in (1) = Coefficient of x in (2)
(1) + (2)
24 x + 24 y = 144
Divide the entire equation by 24, we get
x + y = 6 ------- (3)
(1) - (2)
2x – 2y = -4
By dividing the entire equation by 2, we get
x – y = -2------- (4)
x + y = 6
x – y = -2
---------------
2 x = 4
x = 2
Substitute x = 2 in the (3)
2 + y = 6
y = 6 – 2
y = 4
Hence the solution is (2, 4).
Verification :
13 x + 11 y = 70
13(2) + 11(4) = 70
26 + 44 = 70
70 = 70
Question 2 :
Solve the following system of linear equations by elimination method
65x – 33y = 97 and 33x – 65y = 1
Solution :
65x – 33y = 97 ------- (1)
33x – 65y = 1 ---------(2)
By considering the given equations,
Coefficient of x in (1) = Coefficient of y in (2)
Coefficient of y in (1) = Coefficient of x in (2)
(1) + (2)
98x - 98y = 98
By dividing the entire equation by 98
x - y = 1 ------- (3)
(1) - (2)
32x + 32y = 96
By dividing the entire equation by 32, we get
x + y = 3 ------- (4)
x - y = 1
x + y = 3
---------------
2 x = 4
x = 2
Substitute x = 2 in (3)
2 - y = 1
- y = 1 – 2
y = 1
Hence the solution is (2, 1).
Verification :
65 x – 33 y = 97
65 (2) - 33 (1) = 97
130 - 33 = 97
97 = 97
After having gone through the stuff and examples, we hope that the students would have understood, how to solve pair of linear equations by using elimination method.
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