SOLUTION: Exercise 2.2 #19 on page 97 Solve the system for p and q in terms of x and y. Explain how you could check your solution and perform the check. x=2+p-2q y=3-p+3q I've bee

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Exercise 2.2 #19 on page 97 Solve the system for p and q in terms of x and y. Explain how you could check your solution and perform the check. x=2+p-2q y=3-p+3q I've bee      Log On


   

Question 51233: Exercise 2.2 #19 on page 97
Solve the system for p and q in terms of x and y. Explain how you could check your solution and perform the check.
x=2+p-2q
y=3-p+3q
I've been all over the chapter and couldn't find anything remotely helpful for this. Please help!!!
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
It may be helpful to find a way to eliminate the p, and then eliminate the q, and write two equations, one for p and one for q.

First, if you add the two equations together, you can eliminate the p, and get
x=2+p-2q
y=3-p+3q
x+y = 5 + q, so q = x+y-5

Second, to eliminate the q, multiply both sides of the first equation by 3, and the second equation by 2:
3(x)=3(2+p-2q)
2(y)=2(3-p+3q)

3x= 6 +3p-6q
2y = 6-2p+6q

3x+2y = 12 +p, so p=3x+2y - 12

There you have it:
p=3x+2y-12
q=x+y-5

I have no idea how to check this, unless you solve for x and y to see if you come back with the same equations that you started with. It looks like Linear Algebra to me. Hey, I gotta go to work this morning!!

R^2 at SCC