can you show me how to solve simultaneous equations?

(Depending on what the pupil wants to get out of this session and their ability I will explain the background of simultaneous equations and draw a graph of two lines and sho that their intersection is the point we are effectiveky looking for and refer to this throughout my working). I would give them the example 

3x + 5y = 7, x + y =5

I would argue that multiplying the whole equation by a number means it is the same equation, and say that our aim is to eliminate on of the variables by adding or subtracting one equation from another.

We see that if we multiply the second equation by 5 we get 5x + 5y = 25 and if we tak away the first equation, we get 2x + 0y =18 and so the y part vanishes and by rearranging we can see x=9. no we can change x in both equations to 9, now we only have the y part to look at and we see that, by the second equation 9 + y = 5, so y =-4, now we can check that this is correct by changing x and y to 9 and -4 respectively in  the first equation and see if it works. We get 27 - 20 =7 which is correct. We are done.