SOLUTION: I am really struggling with these type of problems. I have loked at several websoites for CLEAR instructions and this is the oly place but I need to get it in my head. y=2x-2

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: I am really struggling with these type of problems. I have loked at several websoites for CLEAR instructions and this is the oly place but I need to get it in my head. y=2x-2       Log On


   

Question 173339: I am really struggling with these type of problems. I have loked at several websoites for CLEAR instructions and this is the oly place but I need to get it in my head.

y=2x-2
y=-x-1
i now there is a solution cause they meet right? Please say yes!Help me so I can stop struggling.Thanks, Judy (Are they consistent independent with a unique solution? Thats what I had but can't find the pairs.
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
y=2x-2 Start with the first equation


-x-1=2x-2 Plug in y=-x-1. In other words, replace "y" with x+1. What this does is eliminate the "y" term so we can solve for "x".


-x=2x-2%2B1 Add 1 to both sides.


-x-2x=-2%2B1 Subtract 2x from both sides.


-3x=-2%2B1 Combine like terms on the left side.


-3x=-1 Combine like terms on the right side.


x=%28-1%29%2F%28-3%29 Divide both sides by -3 to isolate x.


x=1%2F3 Reduce. So this is the first answer.


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Now that we know the value of "x", we can plug this value into either equation to find the value of "y".


y=2x-2 Go back to the first equation


y=2%281%2F3%29-2 Plug in x=1%2F3


y=2%2F3-2 Multiply


y=-4%2F3 Combine like terms. This is our second answer.



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Answer:


So the solutions are x=1%2F3 and y=-4%2F3 which form the ordered pair


Since we have a unique solution, this means that the system is consistent and independent.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
y=2x-2
y=-x-1
i now there is a solution cause they meet right? Please say yes!Help me so I can stop struggling.Thanks, Judy (Are they consistent independent with a unique solution? Thats what I had but can't find the pairs.
----------------
They are consistent because the slopes are different, so they must
meet at some point.
------------
Since they are both equal to "y", they must be equal to one another.
So 2x-2 = -x-1
3x = 1
x = 1/3
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Since y = x-1, y = -(1/3)-1 = -(4/3)
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Ans: (1/3, -4/3)
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graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C2x-2%2C-x-1%29
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Cheers,
Stan H.