Let (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.

First, find the eq'n of the line connecting (7,8) and (9,0).  The slope of this line is  m = rise / run = (0-8) / (9-7), or m = -8/2, or m = -4.  Thus, the equation of this line is y-0 = -4(x-9), or y = -4x + 36.

We must now solve simultaneously the system y = -4x + 36,  y = 2x - 10.  Let's equate these to one another:  -4x + 36 = 2x - 10.  Thus, 46=6x, or 3x=23, or
x = 23/3.  Subbing this value for x into y = 2x - 10 results in y = 2(23/3) - 30/3, or
y = 16/3.  Thus, the solution is (23/3, 16/3).  a=23/3 and b=16/3.

We are to compute a+b.  This is a+b = 23/3 + 16/3, or 39/3, or 13 (answer).

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