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Solve the following system of equations: 15x + 4y = 61; 4x + 15y = 72 - Mathematics

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Sum

Solve the following system of equations: 15x + 4y = 61; 4x + 15y = 72

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Solution

The given system of equation is

15x + 4y = 61 ….(1)

4x + 15y = 72 ….(2)

Let us eliminate y.

The coefficients of y are 4 and 15.

The L.C.M. of 4 and 15 is 60. So, we make the coefficients of y as 60.

Multiplying (1) by 15 and (2) by 4, we get

225x + 60y = 915 ….(3)

16x + 60y = 288 ….(4)

Substracting (4) from (3), we get

209x = 627 ⇒ x = 3

Putting x = 3 in (1), we get

15 × 3 + 4y = 61 45 + 4y = 61

4y = 61 – 45 = 16 ⇒ y = 4

Hence, the solution is x = 3, y = 4.

Verification: On putting x = 3 and y = 4 in the given equations, they are satisfied. Hence, the solution is correct.

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Elimination Method
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