Use elimination method to find all possible solutions of the following

1.	Use elimination method to find all possible solutions of the following pair of linear equations : 2x + 3y = 8 and 4x + 6y = 7
Answer» 2x + 3y = 8 ......(1) 4x + 6y = 7 .....(2) Step 1 : Multiply Equation (1) by 2 and Equation (2) by 1 to make the coefficients of x equal. Then we get the equations as : 4x + 6y = 16 ......(3) 4x + 6y = 7 .........(4) Step 2 : Subtracting Equation (4) from Equation (3), (4x – 4x) + (6y – 6y) = 16 – 7 i.e., 0 = 9, which is a false statement. Therefore, the pair of equations has no solution.

Use elimination method to find all possible solutions of the following pair of linear equations : 2x + 3y = 8 and 4x + 6y = 7

Answer»

2x + 3y = 8 ......(1)

4x + 6y = 7 .....(2)

Step 1 : Multiply Equation (1) by 2 and Equation (2) by 1 to make the coefficients of x equal. Then we get the equations as :

4x + 6y = 16 ......(3)

4x + 6y = 7 .........(4)

Step 2 : Subtracting Equation (4) from Equation (3),

(4x – 4x) + (6y – 6y) = 16 – 7

i.e., 0 = 9, which is a false statement.

Therefore, the pair of equations has no solution.