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Solve the system y = -x + 7 and y = -0.5(x - 3)2 + 8
y = -x + 7 y = -0.5(x - 3)^2 + 8 replace y in the second equation: -x + 7 = -0.5(x - 3)^2 + 8 -x + 7 = -0.5(x^2 - 6x + 9) + 8 -x + 7 = -0.5x^2 + 3x - 4.5 + 8 0.5x^2 - x - 3x + 7 + 4.5 - 8 = 0 0.5x^2 - 4x + 3.5 = 0 multiple 2 on both sides: x^2 - 8x + 7 = 0 (x - 1)(x - 7) = 0 x = 1 or x = 7 y = -1 + 7 = 6 or y = -7 + 7 = 0 The solution for the system of equations y = -x + 7 and y = -0.5(x - 3)^2 + 8 is (1, 6), (7, 0)
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Asked 4/13/2014 11:02:27 AM
Updated 4/14/2014 2:13:18 PM
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y = -x + 7
y = -0.5(x - 3)^2 + 8
replace y in the second equation:
-x + 7 = -0.5(x - 3)^2 + 8
-x + 7 = -0.5(x^2 - 6x + 9) + 8
-x + 7 = -0.5x^2 + 3x - 4.5 + 8
0.5x^2 - x - 3x + 7 + 4.5 - 8 = 0
0.5x^2 - 4x + 3.5 = 0
multiple 2 on both sides:
x^2 - 8x + 7 = 0
(x - 1)(x - 7) = 0
x = 1 or x = 7
y = -1 + 7 = 6 or y = -7 + 7 = 0
The solution for the system of equations y = -x + 7 and y = -0.5(x - 3)^2 + 8 is (1, 6), (7, 0)
Added 4/13/2014 7:33:01 PM
This answer has been confirmed as correct and helpful.
Confirmed by jeifunk [4/13/2014 7:38:27 PM]
1
y = -x + 7 and y = -0.5(x - 3)2 + 8
Use equation 1 minus equation 2 we get
-x+7+0.5(x-3)^2-8=0
=> -x+7 +0.5(x^2 -6x+9) -8=0
=> -x -1 + 1/2x^2 -3x + 9/2=0
=> 1/2x^2 -4x+ 7/2=0
=> x=7 or x= 1
At x=7 we have y=-7+7 =0
At x=1 we have y=-1+7=6
The answer are ( 7,0) and (1,6)
Added 4/14/2014 2:04:32 PM
This answer has been flagged as incorrect.
Rated good by alonedark2, Flagged by andrewpallarca [4/14/2014 2:12:12 PM]
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alonedark2, please go to unanswered archives to find questions that are not answered yet, or find any questions that has wrong answers to correct.

Duplicate answers are not allowed.
Added 4/14/2014 2:13:18 PM
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