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help with simultaneous equation

Hi so the simultaneous equations are x^2-2xy-y^2=7
x+y=1
I rearranged x+y=1 to get x=1-y
I substituted into the first equation
which i got (1-y)^2 -2y(1-y)-y^2=7
after expanding the brackets and simplifying i got -6-3y+y^2=0
I feel like i have done something wrong as it cant be factorised and I went onto desmos and putting this into a quadratic equation gives me wrong solutions. Have I went wrong expannding brackets?
need help thank you.
Reply 1
Avatar for Zacken
Zacken
22
Original post by 5h3bi
Hi so the simultaneous equations are x^2-2xy-y^2=7
x+y=1
I rearranged x+y=1 to get x=1-y
I substituted into the first equation
which i got (1-y)^2 -2y(1-y)-y^2=7
after expanding the brackets and simplifying i got -6-3y+y^2=0
I feel like i have done something wrong as it cant be factorised and I went onto desmos and putting this into a quadratic equation gives me wrong solutions. Have I went wrong expannding brackets?
need help thank you.


Yeah you expanded wrong, try expanding again more carefully. Post a picture of your working out of the expansion if it still doesn't work.
Reply 2
Avatar for 5h3bi
5h3bi
OP
1
Original post by Zacken
Yeah you expanded wrong, try expanding again more carefully. Post a picture of your working out of the expansion if it still doesn't work.


Now i seem to be getting -6+y+y^2=0
seems to still be wrong
(edited 7 years ago)
Reply 3
Avatar for Zacken
Zacken
22
Original post by 5h3bi
Now i seem to be getting y^2+y-6=0
seems to still be wrong


Like I said, post a picture of your working out for the expansion or type it up.
Reply 4
Avatar for 5h3bi
5h3bi
OP
1
Original post by Zacken
Like I said, post a picture of your working out for the expansion or type it up.

(1-y)^2-2y(1-y)-y^2=7
(1-y) (1-y) when i expand this i get 1-y-y+y as 1*1 is 1, 1* -y is -y and -y again and -y*-y is +y
and when i expand 2y(1-y)
i get 2y-2y^2
so this gives me
1-y-y+y - 2y-2y^2-y^2=7
collecting like terms I get y-2y-y^2=7
subtracting 7 to get
y-2y-y^2-7=0
i keep expanding and getting different answers?
Original post by 5h3bi
(1-y)^2-2y(1-y)-y^2=7
(1-y) (1-y) when i expand this i get 1-y-y+y as 1*1 is 1, 1* -y is -y and -y again and -y*-y is +y



No. (−y)(−y)=y2≠y(-y)(-y)=y^2 \not= y


Original post by 5h3bi

.. - 2y-2y^2-y^2=7


Also no. −2xy=−(2y−2y2)-2xy=-(2y-2y^2)
(edited 7 years ago)
Reply 6
Avatar for Zacken
Zacken
22
Original post by 5h3bi
(1-y)^2-2y(1-y)-y^2=7
(1-y) (1-y) when i expand this i get 1-y-y+y as 1*1 is 1, 1* -y is -y and -y again and -y*-y is +y


This bit is wrong, you get: (1−y)(1−y)=1(1−y)−y(1−y)=1−y−y+y2=1−2y+y2(1-y)(1-y) = 1(1-y) - y(1-y) = 1 - y - y + y^2 = 1- 2y + y^2
Reply 7
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Zacken
22
Original post by leadheadsmith
[...]


No full solutions.
Reply 8
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5h3bi
OP
1
Original post by Zacken
This bit is wrong, you get: (1−y)(1−y)=1(1−y)−y(1−y)=1−y−y+y2=1−2y+y2(1-y)(1-y) = 1(1-y) - y(1-y) = 1 - y - y + y^2 = 1- 2y + y^2

thanks it was due to my careless expanding of brackets, however I will now know for future lessons to carefully expand brackets. Thanks alot for helping Zacken and RDK games.
Reply 9
Avatar for Zacken
Zacken
22
Original post by 5h3bi
thanks it was due to my careless expanding of brackets, however I will now know for future lessons to carefully expand brackets. Thanks alot for helping Zacken and RDK games.


You're welcome!
[QUOTE=Zacken;67647586]No full solutions.

Haven't done simultaneous equations in ages haha

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