Elimination Method

1. .
 Teacher nilvett ferreira

3. LINEAR EQUATIONS IN TWO VARIABLES ARE OF THE
FORM
2x + 3y = 7
14x + 3y = -9
3x - 7y = 11
6x + y = 2

4. Since the topic deals with a pair of linear equations in two
variables , we are going to study two equations at a time.
Solving a pair of linear equations in two
variables means finding the value of x and
finding the value of y

5. Methods of solving a pair of linear equations in
two variables.
1.Elimination method
2.Substitution method
3.Cross multiplication method

6. Solve by elimination method
7x +5y =12
4x + 3y = 9
(1)
(2)
28x + 20y =48
28x + 21y = 63
(-) (-) (-)
-y =-15
y = 15
By using the value of y in equation 1)
The solution is x = -9, y= 15
x 4
x 7
7x + 5y = 12
28x + 20y =48 (3)
(4)
Eqn (3) –eqn (4)
(Taking the opposite coefficients
of x)
Solve by elimination method
7x +5y =12
+ 3y = 9
28x + 21y = 63
7x + 5(15) = 12
7 x + 75 = 12
7 x = 12 - 75
7 x = -63
x = -63
7 , x = -9
Eg 1

7. Solve by elimination method
7x +5y =12
4x + 3y = 9
(1)
(2)
21x + 15y =36
20x + 15y = 45
(-) (-) (-)
x = - 9
By using the value of x in equation 2)
The solution is x = -9, y= 15
x 3
x 5
4x + 3y = 9
21x + 15y =36 (3)
(4)
Eqn (3) –eqn (4)
(Taking the opposite coefficients
of y)
Solve by elimination method
7x +5y =12
4x + 3y 9
20x + 15y = 45
4(-9) + 3y = 9
-36 + 3y = 9
3y = 9 + 36
3 y = 45
y = 45 ,
3 y = 15

8. Solve by elimination method
7x +15y =20
x + 2y = 3
(1)
(2)
7x + 15y =20
7x + 14y = 21
(-) (-) (-)
y =-1
By using the value of y in equation 2)
The solution is x =5, y= -1
x 1
x 7
x + 2y = 3
7x + 15y =20 (3)
(4)
Eqn (3) –eqn (4)
(Taking the opposite coefficients
of x)
Solve by elimination method
7x +15y =20
x + 2y = 3
7x + 14y = 21
x + 2(-1) = 3
x -2 = 3
x = 3 + 2
x = 5
Eg. 2

9. Solve by elimination method
3x +10y = -14
8x - 3y = 22
(1)
(2)
89x = 178
x = 178
89
By using the value of x in equation 1)
The solution is x = 2, y= -2
x 3
x 10
3x + 10y = -14
9x + 30y = -42 (3)
(4)
(Taking the opposite coefficients
of y)
Solve by elimination method
3x +10y = -14
8x - 3y 22
Eg 3
x = 178
89 1
2
x = 2
80x - 30y = 220
3(2) + 10y = -14
6 + 10y = -14
10y = -14 -6
10y = -20
y = -20 ,
10 y = -2
(No need to change the sign since
y coefficients are already opposite)

10. Solve by elimination method ( Try to solve )
(i) 3x + 4y = 5
5x – 2y = -9
(ii) 4x + 3y = 17
5x -2y = 4
(iii) 5x + 7y = -1
2x - 3y = 17
(iv) 2x - 3y = 12
4x - 5y = 22
(v) 7x - 3y = 11
5x - 2y = 8

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