Mathematics

Solve the following systems of simultaneous linear equations by the elimination method
41x + 53y = 135
53x + 41y = 147

20 Likes

Given,

41x + 53y = 135 ……(i)

53x + 41y = 147 …….(ii)

Multiplying eq. (i) by 53 and eq. (ii) by 41 we get,

2173x + 2809y = 7155 ……(iii)

2173x + 1681y = 6027 ……(iv)

Subtracting eq. (iv) from (iii) we get,

⇒ 2173x + 2809y - (2173x + 1681y) = 7155 - 6027

⇒ 2173x - 2173x + 2809y - 1681y = 1128

⇒ 1128y = 1128

⇒ y = 1.

Substituting value of y in eq. (i) we get,

⇒ 41x + 53(1) = 135

⇒ 41x = 135 - 53

⇒ 41x = 82

⇒ x = 2.

Hence, x = 2 and y = 1.

Answered By

12 Likes