Question

Solve the system of equations and choose the correct ordered pair 4x-2y=-2 6x+3y=27

Answer 1

Start with the given
$4x - 2y = - 2 \\ 6x + 3y = 27$
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.
$4x - 2y = - 2 \\ 2x - y = - 1 \\ - y = - 2x - 1 \\ y = 2x + 1$
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!
$y = 2x + 1 \\ 6x + 3y = 27 \\ 6x + 3(2x + 1) = 27 \\ 6x + 6x + 3 = 27 \\ 12x = 24 \\ x = 2$
now that we know what x is, we can plug it back into the first equation!! and we'll get our final answers
$x = 2 \\ y = 2x + 1 \\ y = 2(2) + 1 \\ y = 5$
so our answer will be with the ordered pair (2,5)
$x = 2 \\ y = 5 \\ (2 \: \: \: 5)$