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).
