harder gradient

This is the question:

The gradient of the line joining (-1,3) to (p,q) is -2. The gradient of the line joining (p,q) to (5,2) is -1. Calculate the values of p and q

What I have done is created two equations:

(q-3)/(p--1)=-2
and
(2-q)/(5-p)=-1

But what do I do next?

Quote:

---

Originally Posted by Paulo1913

This is the question:

The gradient of the line joining (-1,3) to (p,q) is -2. The gradient of the line joining (p,q) to (5,2) is -1. Calculate the values of p and q

What I have done is created two equations:

(q-3)/(p--1)=-2
and
(2-q)/(5-p)=-1

But what do I do next?

---

You simplify the two equations:

$\displaystyle \frac{q-3}{p+1} = -2 \Rightarrow q-3=-2(p+1) \Rightarrow q - 3 = -2p - 2$

$\displaystyle \Rightarrow q + 2p = 1$ .... (1)

Do similar with the other.

Then you solve the two equations simultaneously.