Alexander,
I think I know what you mean by "the addition method" so let me illustrate with a different pair of equations.
3x + y = 5
6x  5y = 4
The technique is to select one of the variables, either x or y, and manipulate the equations so that the coefficients of this variable in the two equations have the same value except with opposite signs. So, for example if I multiply both sides of the first equation by 5 then the coefficients of y in the two equations become 5 and 5. I could also multiply the first equation by 2 and then the coefficients of x in the two equations are 6 and 6. I am going to choose that latter.
Multiply both sides of the first equation by 2 to get
6x  2y = 10
6x  5y = 4
Now add the two equations to get
0x  7y = 14 so 7y = 14 and hence y = 2
Now substitute this value into either of the original equations (I am going to use the first equation) and solve for x.
3x + y = 5 so 3x 2 = 5 or 3x = 3 and hence x = 1.
Hence my answer is x = 1, y = 2. You can verify this answer by substituting these values in the second equation to confirm that it is satisfied.
Penny
