Solve the following simultaneous equations: 103x + 51y = 617, 97x + 49y = 583

Question

KnowledgeBoat · Accepted Answer

Given, Equations : 103x + 51y = 617 .......(1), 97x + 49y = 583 .......(2) Adding equations (1) and (2), ⇒ 103x + 51y + (97x + 49y) = 617 + 583 ⇒ 103x + 51y + 97x + 49y = 617 + 583 ⇒ 200x + 100y = 1200 ⇒ 100(2x + y) = 1200 ⇒ 2x + y = ⇒ 2x + y = 12 ........(3) Subtracting equation (2) from (1), ⇒ 103x + 51y - (97x + 49y) = 617 - 583 ⇒ 103x + 51y - 97x - 49y = 34 ⇒ 6x + 2y = 34 ⇒ 2(3x + y) = 34 ⇒ 3x + y = ⇒ 3x + y = 17 ........(4) Subtracting equation 4 from 3, ⇒ 2x + y - (3x + y) = 12 - 17 ⇒ 2x + y - 3x - y = -5 ⇒ -x = -5 ⇒ x = 5. Substituting value of x in equation 1, ⇒ 103x + 51y = 617 ⇒ 103(5) + 51y = 617 ⇒ 515 + 51y = 617 ⇒ 51y = 617 - 515 ⇒ 51y = 102 ⇒ y = = 2. Hence, x = 5, y = 2.

Mathematics

Solve the following simultaneous equations:
103x + 51y = 617, 97x + 49y = 583

Linear Equations

Related Questions

Solve the following simultaneous equations:
23x − 29y = 98, 29x − 23y = 110

Mathematics

Solve the following simultaneous equations:103x + 51y = 617, 97x + 49y = 583

Linear Equations

Related Questions

Solve the following simultaneous equations:23x − 29y = 98, 29x − 23y = 110

Solve the following simultaneous equations:
103x + 51y = 617, 97x + 49y = 583

Solve the following simultaneous equations:
23x − 29y = 98, 29x − 23y = 110