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Solve the following system of linear equations by using the method of elimination by equating the coefficients: 3x + 4y = 25 ; 5x – 6y = – 9 - Mathematics

Sum

Solve the following system of linear equations by using the method of elimination by equating the coefficients: 3x + 4y = 25 ; 5x – 6y = – 9

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Solution

The given system of equation is

3x + 4y = 25 ….(1)

5x – 6y = – 9 ….(2)

Let us eliminate y. The coefficients of y are 4 and – 6.

The LCM of 4 and 6 is 12. So, we make the coefficients of y as 12 and – 12.

Multiplying equation (1) by 3 and equation (2) by 2, we get

9x + 12y = 75 ….(3)

10x – 12y = – 18 …(4)

Adding equation (3) and equation (4), we get

19x = 57 ⇒ x = 3.

Putting x = 3 in (1), we get,

3 × 3 + 4y = 25

⇒ 4y = 25 – 9 = 16 ⇒ y = 4

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

Verification:Both the equations are satisfied by x = 3 and y = 4, which shows that the solution is correct.

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