Question

How do you solve `3x+y=3` and `2y=-6x+6`?

Answer 1

This is an identity, it will work for any values of x and y.

Explanation:

There are several methods for solving simultaneous equations, but in this case I like the idea that `y = y`

If we can get both equations written in terms of `y`, then we can equate them. We have:
`3x + y = 3 " and "2y = -6x +6`

`:." "y = 3-3x " " y= -3x +3`

`y = y rArr " "3-3x = -3x +3`

This simplifies to `" " 0 = 0 " but there is no " x`?

This is an example of an identity which means that there is no single solution and the equations will work for all values of x and y.