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 = β1, y = 2 Β
(c) x = β2, y = 1 Β (d) x = 1, y = 2
CBSE Class 10 Sample Paper for 2022 Boards - Maths Basic [MCQ]
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CBSE Class 10 Sample Paper for 2022 Boards - Maths Basic [MCQ]
Last updated at Sept. 9, 2021 by Teachoo
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 = β1, y = 2 (c) x = β2, y = 1 (d) x = 1, y = 2 Given equations 37π₯ + 43π¦ = 123 β¦(1) 43π₯ + 37π¦ = 117 β¦(2) Adding both equations (1) and (2) (37π + 43π) + (43π + 37π) = 123 + 117 (37π₯ + 43π₯) + (43π¦ + 37π¦) = 240 80π₯ + 80π¦ = 240 80(π + π) = 240 π₯ + π¦ = 240/80 π₯ + π¦ = 3 Now, subtracting (1) and (2) (37π + 43π) β (43π + 37π) = 123 β 117 (37π₯ β 43π₯) + (43π¦ β 37π¦) = 8 β8π₯ + 8π¦ = 8 8(βπ + π) = 8 βπ₯ + π¦ = 8/8 βπ₯ + π¦ = 1 Adding (3) and (4) (π₯ + π¦) + (βπ₯ + π¦) = 3 + 1 2y = 4 y = 4/2 y = 2 Putting y = 2 in (3) π₯ + π¦ = 3 π₯ + 2 = 3 π₯ = 3 β 2 π₯ = 1 β΄ x = 1, y = 2 So, the correct answer is (d)