12x-3y=3
y=4x-1 solve this equation

12x-3y=3
y=4x-1

12x-3(4x-1)=3
12x-12x-3=3
24x=6
x=4

y=4(4)-1
y=15

x=4; y=15

Well first you want to be trying to solve for the same variable in both problems. Lets solve for Y. 
This means we must make both equations say " Y="

first we subtract 12x from both sides of "12x-3y=3"  which leaves us with
-3y=3-12x and y=4x-1.

you are basically going to merge the 2 problems by adding "1" to both problems and then subtracting "4x" from both as well as subtracting "y" from both. This gets rid of a variable in one problem and essentially puts in to the other in the process.

This leaves you with -4y=4-16x
Can you solve from there?