Elimination method 13x 14y 76 32x 13y 73SolutionWe have

Elimination method 1/3x + 1/4y = 7/6 3/2x - 1/3y = 7/3

Solution

We have x/3+y/4 = 7/6.…(1) and 3x/2 –y/3 = 7/3…(2), On multiplying both the sides of the 1^st equation by 24 and the 2^nd equation by 18, we get 8x+6y = 28…(3) and 27x -6y = 42…(4). Now, in order to eliminate y, on adding the 3^rd and the 4^th equations, we get 8x+6y +27x -6y = 28+42 or, 35x = 70 so that x = 70/35 = 2. Then, on substituting x = 2 in the 3^rd equation, we get 8*2 +6y = 28 or, 6y = 28-16 = 12 so that y = 12/6 = 2. Thus, x = 2 and y = 2. We can verify the answer by substituting these values of x and y in any of the original equations.