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JoãoVitorMC
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only if x=0
mathstudent55
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-x is the same as -1x
-4x is -4 x
If you had -1 -4 what do you get?
mathstudent55
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-1 - 4 = ?
EmmaH
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-5?
EmmaH
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im having a lot of trouble with this Solve the system.
y = 2 - x and y = 4x + 7
(1, 1)
(1, 3)
(-1, 3)
(-1, 1)
no solution
im prettyy sure tis no solution
mathstudent55
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Right, so since -1 - 4 = -5, then -x - 4x = -5x
mathstudent55
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Now the system. Again, you have the two equations solved for y already, so use substitution.
mathstudent55
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Do you remember from the two previous systems what to do next?
EmmaH
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yes im working ion it
mathstudent55
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Ok, let me see what you're up to since you're having trouble with it.
EmmaH
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ok so i had 2-x=4x+7
2-x +2=4x+7+2
-x=4x+9
-x-4x=9
now im stuck
mathstudent55
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The 2 on the left side is positive, so you need to subtract 2 from both sides.
seanwalsh1984
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-x (so -1x) take away 4 more x's.
It's like being $1 in the hole in the bank account.
Spend four more bucks, and you are $5 in the whole, not $3.
However...
-x - 4x = 3x is interesting because:
-x - 4x + x = 3x + x
Then we have -4x = 3x
Then as said above, if x = 0, then it is true, otherwise no.
Hope this helps.
mathstudent55
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2 - x = 4x + 7
2 - 2 - x = 4x + 7 - 2
-x = 4x + 5
Now subtract 4x from both sides
EmmaH
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-4-4x=5
mathstudent55
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-x - 4x = 4x - 4x + 5
-5x = 5
EmmaH
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x=-1?
mathstudent55
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|dw:1356283149364:dw|
mathstudent55
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right, x = -1
mathstudent55
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Now insert this value of x in one of the original equations, and solve for y
EmmaH
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sorry i had to do something i do it one sec
EmmaH
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1,3 ?
mathstudent55
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y = 3. You're right, but remember x = -1, not x = 1
EmmaH
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thanks you!
mathstudent55
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|dw:1356283635553:dw|
mathstudent55
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You're welcome.
EmmaH
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one more question The ordered pair (-1, -1) is a solution of the system -4x + 2y = 2 and x + y = -2.
True
False
EmmaH
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i think its true
mathstudent55
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Substitute the ordered pair into both equations. If it makes them both true, it's a solution.
EmmaH
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ok i did it its true
mathstudent55
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-4x + 2y = 2
Try (-1, -1)
Is -4(-1) + 2(-1) = 2 ?
4 - 2 = 2? Yes. The ordered pair works in the first equation.
Now try the second.
x + y = -2
Is -1 + (-1 ) = -1 true?
-2 = -2. It's true.
You are correct, (-1, -1) is a solution.
mathstudent55
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Good job!
EmmaH
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=D