Step by Step help solving a simultaneous equation

Hi all, i am looking to pin point the exact point of intersection of 2 linear equations. my mind seems to have drawn a blank (probably should take a break), but could someone possibly explain the step by step process in which i can solve the following?

y=2x+2
y=(14/3)-(x/3)

The estimates point of intersection from the graph i have drawn is around the (1,4) mark.
Thanks in advance.
Donna

You have two lines. Where they cross, the values of x and y satisfy both equations simultaneously, so it is called a simultaneous system. Like this: http://www.wolframalpha.com/input/?i=plo… There are two ways to find that point. Substitution is when you solve one equation for one variable and substitute that into the other equation. Since both equations are already solved for y, we can set them equal to each other.

2x + 2 = (14/3) - (x/3) The rule is you can do any valid operation on both sides of an equation and it will still be equal. So multiply by three.

6x + 6 = 14 - x Add x, subtract 6.

7x = 8

x = 7/8 Put this into either original equation to find y.

Elimination is when you add the equations in a way to eliminate one variable. Otherwise the process is the same.

just substitute one into the other

2x+2 = (14/3) - (x/3) and solve for x