system of equations

• Oct 22nd 2008, 06:28 PM
I hate Math
system of equations
ok so i suck at this even though its simple...i tend to over think these things....your help would be much appreciated

2p-3q=6
-2p+3q=-6
• Oct 22nd 2008, 06:40 PM
WhoaBlackBetty
It is easy, but you need to find either p or q first and use it to solve for the other one. So, if you have
\$\displaystyle
2p-3q=6
\$
\$\displaystyle -2p+3q=-6
\$
Say you want P for the first equation so you have to get P on one side alone...

\$\displaystyle 2p-3q=6
\$

Divide out your 2 to get P alone.
\$\displaystyle 2p/2=6/2+3q/2\$

Which reduces to p=3+3q/2

Now, you have P so find Q by putting the value of P in the other equation...
\$\displaystyle -2(3+3q/2)+3q=-6\$ and I think you can figure out the rest.
• Oct 22nd 2008, 06:55 PM
runner940
Ok, first you take equation 2 and solve for one of the variables.

Let's solve for 'p'.

-2p+3q=-6
-2p=-3q-6
2p=3q+6
p=3/2q+6/2
p=1.5q+3

Now, take the equation and plug it into the variable of the first equation.

2p-3q=6

2(1.5q+3)-3q=6

Now solve the equation for 'q'.

q=1

Now, plug 'q' into the first equation.

2p-3q=6
2p-3(1)=6
2p-3=6
2p=9
p=4.5

Plug in 'p' and 'q' to check you answers in a equation (it doesn't matter if its the ist or second equation.)

Let's use the first since it look the easiest.

2p-3q=6

2(4.5)-3(1)=6 ?

9-3=6 ?

6=6