Question 398712
Determine the necessary conditions on a, b and c for the following systems to have:
a unique solution; an in finite number of solutions; or be inconsistent. 
x1 + ax2 = 5
3x1 + 6x2 = b
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Put in slope-intercept form:
x1 = -ax2 + 5
slope = -a
int = 5
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x1 = -2x2 - (b/3)
slope = -2
int = (-b/3)
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Unique solution when slopes are not equal:
-a is not equal to -2
a is not equal to 2
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Inconsistent when slopes are equal.
-a = -2
a = 2
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Infinite # of solutions when slopes and int are equal.
a=2 
and (-b/3) = 5
b = -15
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Cheers,
Stan H.