SOLUTION: Consider the system of equations
3x + 4y = 8
6x + ty = s
where t and s are real numbers, find values of s and t so that the system has exactly one solution
Question 932611: Consider the system of equations
3x + 4y = 8
6x + ty = s
where t and s are real numbers, find values of s and t so that the system has exactly one solution Answer by TimothyLamb(4379) (Show Source):
You can put this solution on YOUR website! 3x + 4y = 8
6x + ty = s
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4y = -3x + 8
y = (-3/4)x + 2
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ty = -6x + s
y = (-6/t)x + s/t
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y = (-3/4)x + 2
y = (-6/t)x + s/t
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choose t so the slopes are perpendicular ...
note that perpendicular lines have negative reciprocal slopes:
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-6/t = -1/(-3/4)
6/t = 1/(-3/4)
t = 6*(-3/4)
t = -4.5
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choose s so the y-intercept (s/t) is a nice whole number:
s/t
s/(-4.5)
if s = 4.5 then s/t = -1
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answer:
s = 4.5
t = -4.5
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check:
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3x + 4y = 8
6x - 4.5y = 4.5
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put the system of linear equations into standard form
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3x + 4y = 8
6x - 4.5y = 4.5
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copy and paste the above standard form linear equations in to this solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
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solution:
x = 1.44
y = 0.92
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the system has exactly one solution ...
the above choice of s and t satisfies the problem statement
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