Find intersection?

Question

Find intersection of following equations:
x+y=6
x-y=2
Give answer with explaination,please.

Answer 1

x+y=6 This is equation 1
x-y=2 This is equation 2
so if you use equation 1 to solve the intersection you answer will be like this .
x+y=6
and then x=6-y this is equation 3
you subtitue the equation 3 to equation 2 like this
6-y-y=2
6-2y=2
2y=4
y=2
so you can subtitue the y=2 into equation 1
you will get
x+2=6
x=4
so the answer is x=4 , y=2
But you also can use equation 2 to solve this question .

Answer 2

Each equation gives you an equation for a different line.
It might be handy to first rearrange them into a more user-friendly form of y = ...

So:
x + y = 6
becomes:
y = 6 - x

and

x - y = 2
becomes:
y = x - 2

Then to find the intersection is simply to find a point where they meet. This means a point at which they equal each other. Notice they already have the "y" in common, so you can write the equality as:

6 - x = x -2

Solving for x, by bringing all the "x" onto the same side of the equal sign, and bring all the integers onto the other side:
6 + 2 = x + x
8 = 2x
x = 4

Now that you have x = 4, plug it into any of the equations that the question gave you. Let's choose x + y = 6.

x + y = 6
4 + y = 6
Solving for "y" gives:
y = 6 - 4
y = 2

Hence, you know that they intersect at (4,2)

Answer 3

Add the equations, get 2x = 8 ( the y's cancel).
So x is 4, and using either equation, get y = 2.