# simultaneous equation help

#### tylerdurden

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

#### Prove It

MHF Helper
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.

• tylerdurden

#### eumyang

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
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! • tylerdurden

#### tylerdurden

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.

Last edited:

#### Prove It

MHF Helper
Remember that $$\displaystyle (2x + 3)^2 = (2x + 3)(2x + 3)$$.

Expand it out.

• tylerdurden

#### tylerdurden

4x2 + 6x + 6x + 9

thanks for the help!

Last edited:

#### tylerdurden

not quite sure how you get from

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

to

x= -1 y = 7/5

and why

thanks

Last edited:

#### Prove It

MHF Helper
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 $$\displaystyle 5x+ 7 = 0$$.

• tylerdurden