Question

Solve the simultaneous equations:

a) x + y = 7,  3x - 2y = 11

b) 7x - 2y = 1, 3x + 4y = 15

Answer 1

Solution:

a) We have:

x + y = 7 

                      or,  y = 7 - x        - Eq. I

                    3x - 2y = 11            - Eq. II

 

 

Substitute value of y from Eq. I in Eq. II:

3x - 2 (7 - x) = 11

⇒ 3x - 14 + 2x = 11

⇒ 5x = 11 + 14 = 25

⇒ x = 25/5 = 5

 

Substitute x = 5 in Eq. I:

y  =  7 - 5 =3

 

 

 Thus, the solution of given equations is: x = 5, y = 2

 

a) We have:

                     7x - 2y = 1           - Eq. I

                        3x + 4y = 15        - Eq. II  

 

 

Multiplying Eq. I by 2:

                     14x - 4y = 2           - Eq. III

 

Adding Eq. II and Eq. III:

 17x = 17

⇒ x = 17/17 = 1

 

Substitute x = 1 in Eq. I:

7 (1)- 2y = 1

⇒ 7 - 1 = 2y

⇒ y = 6/2

 Thus, the solution of given equations is: x = 1, y = 3

Thus, the solution of given equations is: a) x = 5, y = 2 and b) x = 1, y = 3