If two endpoints of a segment are (A,B) and (6B, 2A) with a midpoint if (-3,5), what are the values for A and B?

Question

I’m not sure how to solve this problem 

Answer 1

(A+6B)/2 = -3 and (B+2A)/2 = 5

 

So, A+6B = -6

    2A+ B =  10

 

Multiply the first equation by - 2:   -2A - 12B = 12 

                                                    2A +  B   = 10

 

Adding the equations, we have -11B = 22

                                                 B = -2

 

Since A+6B = -6 and B = -2, we get A = 6