How do I use elimination to find the solution of the system of equations y=2x+1 and 2y=4x+2?

Hey there!

To start, you want to manipulate the equations so that they are in standard form ($A x + B y + C = 0$).

To to this, you want all the variable terms on one side, and the constants on the other side. Thus, both equations must be manipulated:

1) $y = 2 x + 1$:

move 2x over to the other side by subtracting 2x from both sides:

$- 2 x + y = 1$

2) $2 y = 4 x + 2$ :

Now manipulate the other equation by moving the 4x over to the other side:

$2 y - 4 x = 2$

You should notice that this equation can be simplified further; all the terms in the equation can be divided by 2.

$y - 2 x = 1$ --> Reorganize so "x" terms are first, y terms are second:

$- 2 x + y = 1$ --> You should notice that both equations ARE THE SAME! This means that there are infinite solutions as the lines are on top of each other!

Hopefully this was of some help and hopefully you've understood this! :)