Simultaneous equations degree two

[DanDan]

Hi, I'm having a bit of trouble with solving simultaneous equations with powers in them. Here is an example and i hope someone can help.

4x = y + 7
3x^2 - 4y = 7

Thanks.

 

[soroban]

Hello, DanDan!

\(\displaystyle \begin{array}{ccc}4x \:= \:y + 7 & [1] \\ 3x^2 - 4y \:=\: 7 & [2] \end{array}\)

With a linear equation and a quadratic equation, Substitution is the suggested method.

Solve [1] for \(\displaystyle y\!:\;y \:=\:4x-7\)

Substitute into [2]: .\(\displaystyle 3x^2 - 4(4x-7) \:=\:7 \quad\Rightarrow\quad 3x^2 - 16x + 21 \:=\:0\)

. . . . \(\displaystyle (x-3)(3x-7) \:=\:0 \quad\Rightarrow\quad x \:=\:\begin{Bmatrix}3 \\ \frac{7}{3} \end{Bmatrix} \quad\Rightarrow\quad y \:=\:\begin{Bmatrix}5 \\ \frac{7}{3}\end{Bmatrix} \)

 

[DanDan]

Thanks

Its so easy now you've explained it! I don't know how I got confused over it now. Thanks so much.