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Question 1071539: Find the value of k so that these lines are coincident.
R:y = 2x + 1
S:x = -6t + k
y = 4t + 2
Line S is an equation system
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! line R is y = 2x + 1
line S is x = -6t + k
you are also given that y = 4t + 2
line R becomes 4t + 2 = 2x + 1
solve for x to get:
x = (4t + 1)/2
you have:
x = -6t + k and x is equal to (4t + 1)/2
this means that:
(4t + 1)/2 = -6t + k
multiply both sides of this equation by 2 to get:
4t + 1 = -12t + 2k
add 12t to both sides of this equation to get:
4t + 1 + 12t = 2k
combine like terms to get:
16t + 1 = 2k
divide both sides of this equation by 2 and solve for k to get:
k = 8t + 1/2
when k = 8t + 1/2, your original equations become:
y = 2x + 1
x = -6t + k
y = 4t + 2
k = 8t + 1/2
since y = 2x + 1 and y = 4t + 2, then you get:
2x + 1 = 4t + 2
since x = -6t + k and k = 8t + 1/2, you get:
x = -6t + 8t + 1/2
2x + 1 = 4t + 2 becomes:
2 * (-6t + 8t + 1/2) + 1 = 4t + 2
combine like terms to get:
2 * (2t + 1/2) + 1 = 4t + 2
simplify to get:
4t + 1 + 1 = 4t + 2
combine like terms to get:
4t + 2 = 4t + 2
the lines are coincident when their equations are the same.
this occurs when k = 8t + 1/2.
this is all based on what i think you are asking because i'm not totally sure that i understood exactly what your problem is asking.
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