Find x+y and x-y 49x-57y=172 57x-49y=252

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Vedu 10th Asked 7 Nov 2026 Student doubt Save WhatsApp Report

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For this question:

Q. Find x + y and x − y, if

49x − 57y = 172 ...(1)

57x − 49y = 252 ...(2)

Solution:

Step 1: Add equations (1) and (2)

(49x − 57y) + (57x − 49y) = 172 + 252

⇒ 49x + 57x − 57y − 49y = 424

⇒ 106x − 106y = 424

⇒ 106(x − y) = 424

⇒ x − y = 424/106

∴ x − y = 4 ...(3)

Step 2: Subtract equation (1) from (2)

(57x − 49y) − (49x − 57y) = 252 − 172

⇒ 57x − 49y − 49x + 57y = 80

⇒ 8x + 8y = 80

⇒ 8(x + y) = 80

⇒ x + y = 80/8

∴ x + y = 10 ...(4)

Final Answer:

x + y = 10

x − y = 4

Doubtly · 8 Nov 2026 Report

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