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# can someone please help me solve this simultaneous equation??!!?

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1. could you be able to go through the steps of achieving the answer because not matter how many times i do it, i can't factorise it or i cant square root it when using the quadratic formula:

8a^2-b^2=2
2a+b=1
2. (Original post by esmeralda123)
could you be able to go through the steps of achieving the answer because not matter how many times i do it, i can't factorise it or i cant square root it when using the quadratic formula:

8a^2-b^2=2
2a+b=1
What were your first/second/maybe even third steps?
3. rearrange the second for b and substitute it into the first. solve for a, find b for both possible results of a.
4. (Original post by SeanFM)
What were your first/second/maybe even third steps?
Firstly i rearranged the linear equation so that it was equal to b

b= 1-2a

and because the quadratic equation states that b must be squared, i squared b=1-2a

1-4a+4a^2

then i added this to the linear equation:

8a^2-1-4a+4a^2=2

i moved the 2 to the left so that the equation is equal to zero

8a^2-1-4a+4a^2-2

then i simplified it to get

12a^2-4a-3=0

i can't factorise this or use the quadratic formula because you can't square root a negative
I'm not even sure if this is correct

can you help me understand what I've done wrong
5. (Original post by esmeralda123)
Firstly i rearranged the linear equation so that it was equal to b

b= 1-2a

and because the quadratic equation states that b must be squared, i squared b=1-2a

1-4a+4a^2

then i added this to the linear equation:

8a^2-1-4a+4a^2=2

i moved the 2 to the left so that the equation is equal to zero

8a^2-1-4a+4a^2-2

then i simplified it to get

12a^2-4a-3=0

i can't factorise this or use the quadratic formula because you can't square root a negative
I'm not even sure if this is correct

can you help me understand what I've done wrong
Be careful, you did it correctly but you can't 'add' 1 - 4a + 4a^2 to the other equation because that itself is not an equation. But I see that you tried to substitute it for b.

You got your signs mixed up at that stage though, if it helps write out the equation just as you substitute b.

After that you have gone wrong thanks to the - sign in front of the brackets - easy mistake to make. Can you see how to do it differently?
6. (Original post by SeanFM)
Be careful, you did it correctly but you can't 'add' 1 - 4a + 4a^2 to the other equation because that itself is not an equation. But I see that you tried to substitute it for b.

You got your signs mixed up at that stage though, if it helps write out the equation just as you substitute b.

After that you have gone wrong thanks to the - sign in front of the brackets - easy mistake to make. Can you see how to do it differently?
yes i understand where i went wrong

do you suggest adding brackets to every linear equation when substituting it to a quadratic equation, when solving non-linear simultaneous equations?
7. (Original post by esmeralda123)
yes i understand where i went wrong

do you suggest adding brackets to every linear equation when substituting it to a quadratic equation, when solving non-linear simultaneous equations?
It doesn't hurt to just to make the substitution absolutely clear to yourself. In this case it is particularly helpful because of the - in front of the b^2.
8. (Original post by SeanFM)
It doesn't hurt to just to make the substitution absolutely clear to yourself. In this case it is particularly helpful because of the - in front of the b^2.
ok
thanks

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