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
---
ty = -6x + s
y = (-6/t)x + s/t
---
y = (-3/4)x + 2
y = (-6/t)x + s/t
---
choose t so the slopes are perpendicular ...
note that perpendicular lines have negative reciprocal slopes:
---
-6/t = -1/(-3/4)
6/t = 1/(-3/4)
t = 6*(-3/4)
t = -4.5
---
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
---
answer:
s = 4.5
t = -4.5
---
check:
---
3x + 4y = 8
6x - 4.5y = 4.5
---
put the system of linear equations into standard form
---
3x + 4y = 8
6x - 4.5y = 4.5
---
copy and paste the above standard form linear equations in to this solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
---
solution:
x = 1.44
y = 0.92
---
the system has exactly one solution ...
the above choice of s and t satisfies the problem statement
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
---
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