Question

How do you find the point of intersection for `3x-y=4` and `6x+2y= -8`?

Answer 1

Intersection point : (0,-4)

Explanation:

We want to find the point `A(X,Y)` like :
`3X-Y=4` and `6X+2Y=-8`

The word "intersection", here, is referring to functions :
A function is generally writing : `y=f(x)`

Then, we need to transform the two equations to something like :
"`y=...`"
Let's define functions `f,g`, who are respectively representing equations `3x-y=4` and `6x+2y=-8`

Function `f` :
`3x - y = 4 <=> 3x = 4 + y <=> 3x-4 = y`
Then we have `f(x)=3x-4`

Function `g` :
`6x + 2y = -8 <=> 2y = -8 - 6x <=> y= -4-3x`
Then we have `g(x)=-3x-4`

`A(X,Y)` is an intersection point between `f` and `g` then :
`f(X) = Y` and `g(X)=Y`
We can mark here `f(X) = g(X)` and more :

`3X-4 = -3X-4`
`<=> 3X = -3X` (we added 4 to each side)
`<=> 6X = 0`
`<=> X = 0`

Then : `A(0,Y)` and `Y=f(0)=g(0)=-4`

The coordinates of `A` is `A(0,-4)`

We can check the result with a graph of the situation (Alone, this is not a proof !!)