Question
Solve the following system of linear equations by using the method of elimination by equating the coefficients: 3x + 4y = 25 ; 5x – 6y = – 9
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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Solution Solve the following system of linear equations by using the method of elimination by equating the coefficients: 3x + 4y = 25 ; 5x – 6y = – 9 Concept: Algebraic Methods of Solving a Pair of Linear Equations - Elimination Method.