Question

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

Answer 1

The given lines intersect at `(0,3)`

Explanation:

[1]`color(white)("XXXX")` `x+y=3`
[2]`color(white)("XXXX")` `2x-y= -3`

add [1] and [2]
[3]`color(white)("XXXX")` `3x = 0`
[4]`color(white)("XXXX")` `x=0`

substituting `0` for `x` in [1]
`color(white)("XXXX")` `0 + y = 3`
`color(white)("XXXX")` `y=3`

Answer 2

I found the point of intersection of coordinates:
`x=0`
`y=3`

Explanation:

You basically solve the System of the two equations trying to find values of `x` and `y` that satisfy both equations simultaneously.
From the first you can isolate `x` as:
`x=3-y`
now you can substitute this `x` into the second equation and find `y` as:
`2(3-y)-y=-3`
`6-2y-y=-3`
`-3y=-9`
`y=3`
substitute back this value into the first equation to find `x`:
`x=3-3=0`