SOLUTION: Consider the equation 3x+2y=6. If possible, find a second linear equation to create a system of equations that has: (25 points) a) Exactly 1 solution. b) Exactly 2 solutions.

Algebra ->  Linear-equations -> SOLUTION: Consider the equation 3x+2y=6. If possible, find a second linear equation to create a system of equations that has: (25 points) a) Exactly 1 solution. b) Exactly 2 solutions.       Log On


   

Question 1021801: Consider the equation 3x+2y=6. If possible, find a second linear
equation to create a system of equations that has: (25 points)
a) Exactly 1 solution.
b) Exactly 2 solutions.
c) No solutions.
d) Infinitely many solutions.
e) For each of the above cases, how many such equations could you find? Explain.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
No solutions : parallel line (infinitely many choices, here I choose 10 as the right hand side)
3x%2B2y=10
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Infinitely many solutions : a multiple of the line (infinitely many choices, here I choose 2 as the multiplier)
2%283x%2B2y%29=10%29
6x%2B4y=20
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Exactly one solution (any combination that is neither the same coefficients or a multiple of them) (infinitely many choices, you can change 5,7, and 11)
5x%2B7y=11
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Exactly 2 solutions : Not possible (none)