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.
Is there an error in this question or solution?
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.
