Simultaneous Question

Use substitution. First try to figure out how many p's one q is worth.

If 2 q's are worth 3 p's. How much is one worth? Answer: q = 1.5p.
(That's called "solving for q.")

So where you see q in the second equation, you can substitute 1.5p:
4p + 1.5p + 11 = 0.

Combining like terms gives you 5.5p + 11 = 0.
Solving for p gives you p = -2.

Now put the value of p back into the first equation:
3(-2) = 2q.

Solving for q gives us: q = -3.

----------------------------
Summary of overall strategy:
--Figure out what q is worth in terms of p, using the first equation.
--Rewrite the second equation, putting some multiple of p where q is.
--Solve the second equation for p.
--Figure out q.

Thank you so much for helping me

Another common method is called elimination

e.g.
3p = 2q
4p +q + 11 = 0

becomes
3p - 2q=0
4p +q + 11 = 0

four times the first equatio and triple the second becomes
12p-8q=0
12p+3q + 33 = 0

Subtract the first from the second

11q+33=0

rearrange

11q=-33

and solve

q=-3

so p=-2

now check the answer

3(-2) = 2(-3) check
4(-2) +(-3) + 11 =-8-3+11=-(8+3)+11=-11+11=0 check

BTW elimination is better done by using matrix notation

3p = 2q
4p +q + 11 = 0

becomes
[3 -2] [p] [ 0]
[4 1] [q] [-11]

Rap

So for simultaneous equations you can use the elimination method as well, thanks for the reply

Yes

There also a graphical method

the two equations
3p = 2q
4p +q + 11 = 0

are also lines in thd p:q plane
q=3/2p and q=-4p-11

if you were to plot these two lines in this plane thery would intersect ar a point (p0,q0) . This point would be the solution to the simultaneous equations.

Rap

Cool thanks for showing me both methods