# Math Help - Simultaneous Equation help!

1. ## Simultaneous Equation help!

I need to solve this simultaneous equation. Im not sure whether to use the substitution method or the elimination method. Can someone get me started, or even better let me know the full working and answer.

2p^2 - 3q^2 = 2
2p + q = 14

2. Originally Posted by nugiboy
I need to solve this simultaneous equation. Im not sure whether to use the substitution method or the elimination method. Can someone get me started, or even better let me know the full working and answer.

2p^2 - 3q^2 = 2 [1]
2p + q = 14 [2]
Unless both equations are linear, it is hard to use elimination. The first equation isn't linear, so we will use substitution.

From [2] we have:

$q=14-2p$

Sub into [1]:

$2p^2-3(14-2p)^2=2$

$2p^2-(12p^2-168p+588)=2$

$-10p^2+168p-590=0$

$5p^2-84p+295=0$

$p=5$ or $p=\frac{59}{5}$

Substituting those back into [2] we get:

$q=4$ or $q=-\frac{48}{5}$

Answer: $p=5$, $q=4$ or $p=\frac{59}{5}$, $q=-\frac{48}{5}$

3. If I was marking this paper you would get points off. Because you should pair the p and the q in a solution set.

4. Do you mean $\lbrace (p,q): (5,4),(\frac{59}{5},-\frac{48}{5}) \rbrace$?

5. Originally Posted by ThePerfectHacker
If I was marking this paper you would get points off. Because you should pair the p and the q in a solution set.

You would take points off because they used one correct solution instead of your correct solution?????

If so, I sincerely hope you are not an exam marker.

6. Originally Posted by oaksoft
You would take points off because they used one correct solution instead of your correct solution?????
No, because he did not pair the solutions. He fixed it in his other post.

If so, I sincerely hope you are not an exam marker.
Then do everything correctly.