i'd be really grateful if someone could complete this simultaneous equation with working out explaining each stage of the process. thanks.

y = 2x + 3

x2 + y2 = 2

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- Jul 3rd 2010, 05:58 AMtylerdurdensimultaneous equation help
i'd be really grateful if someone could complete this simultaneous equation with working out explaining each stage of the process. thanks.

y = 2x + 3

x2 + y2 = 2 - Jul 3rd 2010, 06:04 AMProve It
I assume that the two equations are:

$\displaystyle y = 2x + 3$ and $\displaystyle x^2 + y^2 = 2$.

Substituting into equation 2 gives

$\displaystyle x^2 + (2x + 3)^2 = 2$.

Now expand, collect like terms, and solve. - Jul 3rd 2010, 06:08 AMeumyang
You mean this?

$\displaystyle y\,=\,2x\,+\,3$

$\displaystyle x^2\,+\,y^2\,=\,2$

Plug the first equation into the second where you see the y:

$\displaystyle x^2 + (2x + 3)^2 = 2$

Solve for x:

$\displaystyle x^2 + 4x^2 + 12x + 9 = 2$

$\displaystyle 5x^2 + 12x + 7 = 0$

$\displaystyle (x + 1)(5x + 7) = 0$

Set each factor equal to 0 and you'll get

$\displaystyle x = -1$ or $\displaystyle x = {-\frac{7}{5}}$

Plug both values into the first equation to get the corresponding y values.

EDIT: Beaten to it! ;) - Jul 3rd 2010, 06:20 AMtylerdurden
cheers guys. appreciate the help.

the only bit i'm not too sure on is how to get from

x2 + (2x+3)2 = 2 to

x2 + 4x2 + 12x = 9 =2

would really appreciate if you could explain what i have to do.

thanks. - Jul 3rd 2010, 06:35 AMProve It
Remember that $\displaystyle (2x + 3)^2 = (2x + 3)(2x + 3)$.

Expand it out. - Jul 3rd 2010, 06:57 AMtylerdurden
4x2 + 6x + 6x + 9

thanks for the help! - Jul 3rd 2010, 07:55 AMtylerdurden
not quite sure how you get from

(x+1) (5x +7) = 0

to

x= -1 y = 7/5

and why

thanks - Jul 3rd 2010, 06:04 PMProve It
When you have two numbers being multiplied together to give $\displaystyle 0$, that means at least one of them has to be $\displaystyle 0$.

So if $\displaystyle (x + 1)(5x + 7) = 0$ then $\displaystyle x + 1 = 0$ or $\displaystyle 5x+ 7 = 0$.