Solve the following pair of equations 2x 3y 1 3x 2y 9Sol

Solve the following pair of equations:

2x - 3y = 1

3x - 2y = 9

Solution

We are given the equatuions 2x - 3y = 1...(1) and 3x - 2y = 9...(2) On multiplying both the sides of the 1st equation by 2 and the 2nd equation by 3, we get 4x - 6y = 2...(3) and 9x - 6y = 27...(4). Now, on subtracting the 3rd equation from the 4th equations, we get 9x - 6y - 4x + 6y = 27 - 2 or, 5x = 25. Therefore x = 25/5 = 5 . Then , on substituting x = 5 in the 1st equation, we get 2*5 - 3y = 1 or, 3y = 10 - 1 = 9 so that y = 9/3 = 3. Thus, the answer is x = 5 and y = 3. We can verify this result by substituting x = 5 and y = 3 in the 2nd equation.