Intersection of two lines - Have I got it right? I have been asked to solve where these two lines intersect, it has been a very long time since I have done this, my numbers seem too big. Can someone check these for me?
2x + y = 6
x + 2y = 12

    (find x)                          (plug into first equation)
    x + 2y = 12                       2(-2y+12)+y=6
    x = -2y + 12                      -4y+24+y=6
                                      -3y=6-24
                                      -3y=18
                                       3y=18
                                       y=18-3
                                       y=15

    (put y back in)
    x=-2(15)+12
    x=-30+12
    x=-18

Intersection at (-18,15)


By elimination:
$$\begin{cases}2x + y = 6,\\
    x + 2y = 12.\end{cases}$$
Subtract twice the first equation from the second and get
$$-3x=0.$$

By substitution:
From the first equation, $y=6-2x$, and plugging in the second, $x+12-4x=12$, giving $$-3x=0.$$

By Cramer:
$$x=\frac{\begin{vmatrix}6&1\\12&2\end{vmatrix}}{\begin{vmatrix}2&1\\1&2\end{vmatrix}}=0.$$

In all three cases, $y=6$ by the first equation.
