SOLUTION: find A and B so that the system below has the solution (2,3) Ax-2By=6 3Ax-By=-12 thanks for all the help :) appriciate it

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons  -> Linear Equations Lesson -> SOLUTION: find A and B so that the system below has the solution (2,3) Ax-2By=6 3Ax-By=-12 thanks for all the help :) appriciate it      Log On


   

Question 708040: find A and B so that the system below has the solution (2,3)
Ax-2By=6
3Ax-By=-12
thanks for all the help :)
appriciate it
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Use the required point in both equations, simplify, and solve the resulting system.

A(2)-2B(3)=6
3A(2)-B(3)=-12

System to solve, but...
2A-6B=6
6A-3B=-12

Divide the first by 2, and the second by 3:
System to solve:
A-3B=3
2A-B=-4

Multiply all of the first by 2, subtract the second from the first:
highlight%28B=-2%29, so you can pick any equation from the simplest system just found and find A. highlight%28A=-3%29.