SOLUTION: Function f satisfies f(x)+2f(5-x)=x for all real numbers x. What is the value of f(1)?

At x= 1 you have  f(1) + 2f(4) = 1    (1)

at x= 4 you have  f(4) + 2f(1) = 4    (2)



Write it as the 2x2-system of linear equations in STANDARD form


     f(1) + 2f(4) = 1     (1')

    2f(1) +  f(4) = 4     (2')


Multiply equation (2') by 2;  keep equation (1') as is


     f(1) + 2f(4) = 1     (1'')

    4f(1) + 2f(4) = 8     (2'')


From equation ((2''), subtract equation (1'')


     3f(1)        = 7

      f(1)        = .      ANSWER