Answer
$(11,-1/2)$
Substitution was more efficient.
Please see the graph.
Work Step by Step
$y = 1/2 * x -6$
$2x+6y = 19$
$2x+6y = 19$
$2x+6*(1/2 * x -6) = 19$
$2x + 3x -36 = 19$
$5x - 36 = 19$
$5x -36+36 = 19+36$
$5x = 55$
$5x/5 = 55/5$
$x = 11$
$y = 1/2*x -6$
$y = 1/2 * 11 -6$
$y = 11/2 - 6$
$y = 11/2 - 12/2$
$y = -1/2$
The graph was made using graphing software.
Green line: $2x+6y=19$
Blue line: $y=.5x-6$
