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

Jul 4, 2016

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:
$3 x + y = 3 \text{ and } 2 y = - 6 x + 6$

$\therefore \text{ "y = 3-3x " } y = - 3 x + 3$

$y = y \Rightarrow \text{ } 3 - 3 x = - 3 x + 3$

This simplifies to $\text{ " 0 = 0 " but there is no } x$?

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.