could some one help me with this question?!?!

When solving a system of equations, there are three possible solutions: a unique solution, no solution, or an infinite number of solutions. Use three or more sentences to describe each type of possible solution. For each type of solution, please describe what the graph would look like as well as what the algebraic solution would look like.

Question

could some one help me with this question?!?!


When solving a system of equations, there are three possible solutions: a unique solution, no solution, or an infinite number of solutions. Use three or more sentences to describe each type of possible solution. For each type of solution, please describe what the graph would look like as well as what the algebraic solution would look like.

anonymous · Answer

Question
 2x+3y=17
 y=6x-21
 
17-9x=18y
 12y=11-6x
 
3x-y=13
 2y=6x-26 


Answer
 2x + 3y = 17
 y = 6x - 21
 
2x + 3y = 17
 3y = -2x + 17
 y = (-2/3)x + (17/3)
 
(-2/3)x + (17/3) = 6x - 21
 -2x + 17 = 18x - 63
 -20x = -80
 x = 4
 
y = 6(4) - 21
 y = 24 - 21
 y = 3
 
Unique solution
 x = 4
 y = 3
 
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17 - 9x = 18y
 -9x + 17 = 18y
 y = (-1/2)x + (17/18)
 
12y = 11 - 6x
 12y = -6x + 11
 y = (-1/2)x + (11/12)
 
Same slope, but different y-intercepts
 
No Solution
 
-------------------------
 
3x - y = 13
 2y = 6x - 26
 
3x - y = 13
 -y = -3x + 13
 y = 3x - 13
 
2y = 6x - 26
 y = 3x - 13
 
Same slope and same y-intercept
 

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 I'm not sure what a unique solution is... but no solution means there is no answer to the equation, the variables are not a solution, therefore on the graph the different lines of the equations will never cross. infinite solutions means that theres and unknown number of solutions, it goes on and on, the graph will be the lines of the equations will be on top of eachother.

anonymous · Answer

In a unique solution, the lines of each equation intersect at one point on a graph. The solution is (x, y), where x and y are definite numbers.
 
In no solution, the lines do not intersect at all. They are parallel and have the same slope.
 
In infinitely many solutions, the lines are exactly the same. There is no exact point for a solution; x and y could be any real number.

anonymous · Answer

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anonymous · Answer

n a unique solution, the lines of each equation intersect at one point on a graph. The solution is (x, y), where x and y are definite numbers.

In no solution, the lines do not intersect at all. They are parallel and have the same slope.

In infinitely many solutions, the lines are exactly the same. There is no exact point for a solution; x and y could be any real number.

anonymous · Answer

thanks guys!!!!

anonymous · Answer

that's what I said colo