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
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
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:
$\displaystyle q=14-2p$
Sub into [1]:
$\displaystyle 2p^2-3(14-2p)^2=2$
$\displaystyle 2p^2-(12p^2-168p+588)=2$
$\displaystyle -10p^2+168p-590=0$
$\displaystyle 5p^2-84p+295=0$
$\displaystyle p=5$ or $\displaystyle p=\frac{59}{5}$
Substituting those back into [2] we get:
$\displaystyle q=4$ or $\displaystyle q=-\frac{48}{5}$
Answer: $\displaystyle p=5$, $\displaystyle q=4$ or $\displaystyle p=\frac{59}{5}$, $\displaystyle q=-\frac{48}{5}$