Math Is Fun Forum

planetdomi

Member

Registered: 2011-09-17

Posts: 16

Simultaneous Equations

Through using substitution how can I solve

3p-3 = q
and
7p=1+4q

so that p=-1 and q=-2

Many Thanks in advance

planetdomi

Member

Registered: 2011-09-17

Posts: 16

Re: Simultaneous Equations

So sorry I go the equations wrong

3p-3=3q

and

7p = 1+4q

thanks

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Simultaneous Equations

hi planetdomi

There are several methods for solving a pair of equations like these, but essentially, they all involve eliminating one of the unknowns  and in the process reducing the number of equations from two down to one.  Then you would just solve that equation for the remaining unknown.  Once you have that done you can use that value to substitute into either of the equations to solve for the other unknown.

EDIT: I dear!  I've just re-read your post.  You wanted the substitution method, didn't you, and what follows isn't substitution.  Never mind, I'll leave it as a post and do a second post where I'll do it by substitution.  That'll teach me to read the question properly!

In this pair of equations, some advance simplification is possible (the top one has a common factor of 3) but I'll disregard that as it will be more useful to you for the next problem if you see my method as if there wasn't any simplification.

So here we go.

I'll aim to remove 'p' from the equations.  To do that I'll try to make both equations have equal amounts of 'p', then I can eliminate it.

I've multiplied all by 7.

and

I've multiplied all by 3 this time.  That makes 21p in both so I can subtract the left hand sides and the right hand sides of the new equations, so removing the 'p' by 21p - 21p.

Now to solve that for q.

Now substitute that value for q into the original first equation.

So, in general, look at the  numbers multiplying 'p' in the two equations.  Times the second equation by whatever number was in front of 'p' in the first equation ( 7 ) and times the first equation by whatever number was in front of 'p' in the second equation ( 3 ).  Then you can subtract away to zero the 'p' terms.

Hope that helps. 

Bob

Last edited by Bob (2011-09-24 20:21:56)

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Simultaneous Equations

Now by substitution.

Now, replace the 'p' in the second equation by this expression containing q.

simplify and solve for q.

Now I've got 'q'  I can do as I did above to find 'p'.

Looking at the two methods, I really don't know why I choose the other method for this problem.  This was much shorter wasn't it! 

Sometimes that method is easier though, so I tend to switch between them.

Bob

Last edited by Bob (2011-09-24 20:18:33)

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

planetdomi

Member

Registered: 2011-09-17

Posts: 16

Re: Simultaneous Equations

Thank you

As ever that explains things beautifully.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Simultaneous Equations

You're welcome.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob