Step II : Multiplying the given equation so as to make the co-efficients of the variable to be eliminated equal.
Step III : Add or subtract the equations so obtained in Step II, as the terms having the same co-efficients may be either of opposite or the same sign.
Step IV : Solve the equations in one varibale so obtained in Step III.
Step V : Substitute the value found in Step IV in any one of the given equations and then copmpute the value of the other variable.
Let us decide to eliminate x from the given equation. Here, the co-efficients of x are 4 and 2 respectively. We find the L.C.M. of 4 and 2 is 4. Then, make the co-efficients of x equal to 4 in the two equations.
Hence, the solution of the system of equations is x = , y = .
Hence, the solution of the system of equations is, x = , y = .
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.
19x = 57 ⇒ x = 3.
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.
Verification : On putting x = 3 and y = 4 in the given equations, they are satisfied. Hence, the solution is correct.