Simultaneously solve these equations 3x+y=7 and 3x-y=5

Method 1 (Elimination) -

You can see that If you add the 2 equations together you can eliminate the y variable like so 6x=12, then if you divide both sides by 6 you get x=2. Then if you place x=2 back into either of the equations you get y=1.

Method 2 (Substitution) -

Take equation 1 and rearrange it so you get y in terms of x, so all the y's on one side and all the x's on the other side. You get y=7-3x. Take this expression for y and put it into equation 2, 3x-y=5. You get 3x - (7-3x) = 5. If you expand out the brackets you get 6x-7=5 and so 6x=12 then dividing both sides by 6, x=2. Like before place x=2 into either equation to get y=1.