Question

How do you solve the system `6x-2y=2` and `9x-3y=1`?

Answer 1

The given equations represent parallel lines with no intersection point (and therefore no solution).

Explanation:

[1]`color(white)("XXXX")` `6x-2y= 2`
`color(white)("XXXX")` `color(white)("XXXX")` `rArr 3x-y = 1`
[2]`color(white)("XXXX")` `9x-3y = 1`
`color(white)("XXXX")` `color(white)("XXXX")` `rArr 3x-y = 1/3`

Since equations [1] and [2] give two different values for `(3x-y)` they represent non-intersecting (parallel) lines.