math
posted by Tiff .
the system of linear equations below has a unique solution for all but one value of a:
6 x−12 y=−6
58 x+a y=−58
What is this exceptional value for a?

unique solution means the lines intersected at only one point (intersecting lines),, thus lines that do not intersect don not have a solution (parallel lines)
if two lines are parallel, then their slopes must be equal,, thus get their slopes by writing them into the form:
y = mx + b
where m = slope, and b = yintercept
*for 6x − 12y = −6,
6x − 12y = −6
12y = 6  6x
y = (1/2)x + (1/2)
thus m = 1/2
*for 58x+ ay = −58,
58x+ ay = −58
ay = 58  58x
y = (58/a)x  58/a
thus m = 58/a
equating and solving for a:
1/2 = 58/a
a = 116
so there,, :) 
the answer