Posted by **Tiff** on Tuesday, October 26, 2010 at 12:42am.

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?

- math -
**jai**, Tuesday, October 26, 2010 at 12:57am
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 = y-intercept

*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,, :)

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