If the points P(−3, 9), Q(a, b) and R(4, −5) are collinear and a + b = 1, find the values of a and b.

Let A(x1 = −3, y1 = 9), B(x2 = a, y2 = b) and C(x3 = 4, y3 = −5) be the given points.
The given points are collinear if

$x_{1}\left(y_{2}-y_{3}\right)+x_{2}\left(y_{3}-y_{1}\right)+x_{3}\left(y_{1}-y_{2}\right)=0$

$\Rightarrow(-3)(b+5)+a(-5-9)+4(9-b)=0$

$\Rightarrow-3 b-15-14 a+36-4 b=0$

$\Rightarrow 2 a+b=3$

Now, solving a + b = 1 and 2a + b = 3, we get a = 2 and b = −1.
Hence, a = 2 and b = −1.