Answer
$(-12, -5)$, $(-12, 5)$, $(12,-5)$, $(12,5)$
Work Step by Step
$x^2+y^2=169$
$5x+12y=0$
$5x+12y=0$
$5x+12y-12y=0-12y$
$5x=-12y$
$5x/5=-12y/5$
$x=-12y/5$
$x^2+y^2=169$
$(-12y/5)^2+y^2=169$
$144y^2/25+y^2=169$
$169y^2/25=169$
$169y^2*25/25=169*25$
$169y^2=169*25$
$169y^2/169=169*25/169$
$y^2=25$
$\sqrt {y^2} =\sqrt {25}$
$y=±5$
$x^2+y^2=169$
$x^2+25=169$
$x^2+25-25=169-25$
$x^2=144$
$\sqrt {x^2} = \sqrt {144}$
$x=±12$
