start with the given
[tex]4x - 2y = - 2 \\ 6x + 3y = 27[/tex]
let's focus on the top equation first, we want to get either x or y alone. y would be easier here so let's do that.
[tex]4x - 2y = - 2 \\ 2x - y = - 1 \\ - y = - 2x - 1 \\ y = 2x + 1[/tex]
here we simply divided everything by 2, then solved for y.
now we're going to plug this y into the second equation so that we only have an x!
[tex]y = 2x + 1 \\ 6x + 3y = 27 \\ 6x + 3(2x + 1) = 27 \\ 6x + 6x + 3 = 27 \\ 12x = 24 \\ x = 2[/tex]
now that we know what x is, we can plug it back into the first equation!! and we'll get our final answers
[tex]x = 2 \\ y = 2x + 1 \\ y = 2(2) + 1 \\ y = 5[/tex]
so our answer will be with the ordered pair (2,5)
[tex]x = 2 \\ y = 5 \\ (2 \: \: \: 5)[/tex]
