Help URGENT!

By addition method, it is the same thing as elimination, which is what it is officially called.

Elimination:

So we can mulitply the bottom equation by 2 so that we can then cancle out the "x's" later on

(2x+3y=19)*2

4x+6y=38

Now we have the two equations

4x-y=3 , 4x+6y=38

We can then subtract these two equations to cancel out the "x"

4x-y-(4x+6y)=3-38

-y-6y=-35

-5y=-35

5y=35

y=7

So now we have figured out our y value is 7, and we can substitute it into our equation to get our "x" value now.

4x-7=3

4x=10

x=5/2 or 2.5 

Multiply the first equation by  3  ⇒   12x -3y   =  9

Add this to the second equation and we get

14x = 28      divide both sides by 14

x = 2

And using  4(2) - y  = 3   ⇒   8 - y  = 3 ⇒    y  = 5

So

{x, y }  = { 2 , 5 }