If p+q = 4, q+r = - 2, r+p = 3 then p+q+r = ?

a) 2/5 b) 5/2 c) 6/2 d) 5 e) 6

5/2

Step-by-step explanation:

We are looking for p+q+r.

We are given:

p+q = 4 Equation 1.

q+r=-2 Equation 2.

p + r=3. Equation 3.

I'm going to solve the first equation for p giving me p=4-q.

I'm going to solve the second equation for r giving me r=-2-q.

I'm going to plug this into the third equation.

p + r=3

(4-q) + (-2-q) = 3

4-q+-2-q=3

Combine like terms:

2-2q=3

Subtract 2 on both sides:

-2q=1

Divide both sides by - 2:

q=-1/2.

Plug into the first equation to find p now.

First equation is p+q=4 with q=-1/2.

p+q=4

p + (-1/2) = 4

Add 1/2 on both sides

p=4+1/2

p=9/2.

Let's find r now.

Using the second equation with p=9/2 and/or q=-1/2 we have:

q+r=-2

-1/2+r=-2

Add 1/2 on both sides

r=-2+1/2

r=-3/2

So what is p+q+r?

Let's plug in our p, q, and r and find out!

p+q+r

9/2+-1/2+-3/2

9/2-4/2

5/2