SOLUTION: 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

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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