Check sibling questions

What is the solution of the pair of linear equations 37x + 43y = 123, 43x + 37y = 117?

(a) x = 2, y = 1Β  Β  Β (b) x = βˆ’1, y = 2 Β 

(c) x = βˆ’2, y = 1 Β  (d) x = 1, y = 2

Slide72.jpeg

Slide73.jpeg
Slide74.jpeg


Transcript

Question 40 What is the solution of the pair of linear equations 37x + 43y = 123, 43x + 37y = 117? (a) x = 2, y = 1 (b) x = βˆ’1, y = 2 (c) x = βˆ’2, y = 1 (d) x = 1, y = 2 Given equations 37π‘₯ + 43𝑦 = 123 …(1) 43π‘₯ + 37𝑦 = 117 …(2) Adding both equations (1) and (2) (37𝒙 + 43π’š) + (43𝒙 + 37π’š) = 123 + 117 (37π‘₯ + 43π‘₯) + (43𝑦 + 37𝑦) = 240 80π‘₯ + 80𝑦 = 240 80(𝒙 + π’š) = 240 π‘₯ + 𝑦 = 240/80 π‘₯ + 𝑦 = 3 Now, subtracting (1) and (2) (37𝒙 + 43π’š) βˆ’ (43𝒙 + 37π’š) = 123 βˆ’ 117 (37π‘₯ βˆ’ 43π‘₯) + (43𝑦 βˆ’ 37𝑦) = 8 βˆ’8π‘₯ + 8𝑦 = 8 8(βˆ’π’™ + π’š) = 8 βˆ’π‘₯ + 𝑦 = 8/8 βˆ’π‘₯ + 𝑦 = 1 Adding (3) and (4) (π‘₯ + 𝑦) + (βˆ’π‘₯ + 𝑦) = 3 + 1 2y = 4 y = 4/2 y = 2 Putting y = 2 in (3) π‘₯ + 𝑦 = 3 π‘₯ + 2 = 3 π‘₯ = 3 βˆ’ 2 π‘₯ = 1 ∴ x = 1, y = 2 So, the correct answer is (d)

Davneet Singh's photo - Teacher, Engineer, Marketer

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.