+501 Let $P=(a,b)$ be the point of intersection of the line $y=2x-10$ and the line through $(7,8)$ and $(9,0)$. Compute $a+b$.
+129852 Slope of line through the given points = -8/2 = -4
Equation of this line is
y = -4(x + 9)
y = -4x + 36
Compute the x intersection of both lines
2x - 10 = - 4x + 36
2x + 4x = 36 + 10
6x = 46
x = 46/6 = 23/3
And the y intersection = -4(23/3) + 36 = 16/3
So (a, b) = ( 23/3 , 16/3) and a + b = 23/3 + 16/3 = 39/3 = 13
