SOLUTION: find values of A and B so that the graph of the given equation will contain the give points: Ax+By=3;(8,3)and(13,7)

Algebra ->  Linear-equations -> SOLUTION: find values of A and B so that the graph of the given equation will contain the give points: Ax+By=3;(8,3)and(13,7)      Log On


   

Question 360039: find values of A and B so that the graph of the given equation will contain the
give points: Ax+By=3;(8,3)and(13,7)
Answer by Jk22(389) About Me  (Show Source):
You can put this solution on YOUR website!
Ax + By = 3

a) x = 8, y = 3, plugged in the equation : 8A + 3B = 3

b) x = 13, y = 7 gives the equation : 13A + 7B = 3


equ 7(a)-3(b) eliminates the B : 7*8A-3*13A = 7*3 - 3*3

(56 - 39)A = 21 - 9

17A = 12

A = 12 / 17 (a)=> B = (3 - 8*12/17)/3 = (51 - 96)/17/3 = -45/17/3 = -15 / 17

(b)=> B = (3 - 13*12/17)/7 = (51 - 156)/17/7 = -105/17/7 = -15 / 17


the equation is : 3/17(4x-5y) = 3

4x - 5y = 17



Verification :

3/17*(4*8 - 5*3) = 3/17*(32 - 15) = 3/17*17 = 3

3/17*(4*13 - 5*7) = 3/17*(52 - 35) = 3/17*17 = 3