Question

How do you solve this system of equations: `2x - 6y = 12;- 5x + 15y = - 31`?

Answer 1

You do not have solutions.

Explanation:

The two equtions represent two parallel lines so they will not have points in common (and hence solution of the system). You can see this because if you write them in the form `y=mx+c` where `m` is the slope you get:
`y=1/3x-2`
`y=1/3x-31/15`

They have both the same slope and differ only in the `y-`intecept.

You can also try to solve the system and, say, try to isolate `x` from the first equation:

`x=6/2y+12/2`

`x=3y+6`

and substitute into the second equation:

`-5(color(red)(3y+6))+15y=-31`

solve for `y`:

`cancel(-15y)-30+cancel(15y)=-31` not true!

Graphically: